I love this subject! I'm studying Bayesian methods in my PhD, here's my perspective: Frequentist reasoning wants to deal objectively with data, so it considers probability to be a property of the world; it says "the coin has probability 1/2 of being heads because that's the frequency of heads in the behavior of this coin"... and there's a right probability, it's a fact from the world, it can be learned by data that shows that frequency in behavior. Data is noisy, but it reveals true propensities through frequencies. Bayesian reasoning wants to deal logically with data, so it considers probability to be a property of logical propositions about the world; it says "the statement 'coin landed heads' has a certain probability of being true, it is 1/2 for me and 0 or 1 for you depending on what you see"... the proposition is connected to a point of view, and different points of view will differ in how close they are to the truth about the state of the coin. So probability is subjective in a sense, but all points of view with equal information should objectively agree about probabilities of their statements (it's objectively subjective, just recognizing the existence of different points of view, but they are not supposed to be personal, not opinions). When you update your "belief" over data, it's because data moved your point of view in relation to the "truth". In this example, once we see the coin, we update the statement "coin landed heads" from 1/2 to 0 or 1 depending on what we see (probabilities of 0 and 1 mean perfect information while 1/2 means no information). There isn't an actual divide between the two, theoretically... Bayesian reasoning recognizes the relation between frequency and plausibility, while frequentist reasoning recognizes points of view, it just doesn't go there.
So in other words the frequentists approach will give you a correct answer every time but may need indefinitely to evaluate, while the bayesian approach gives you a result immediately but this result may be wrong.
@@ndrsvgl hm... the approaches are answering different questions, both correctly... what is this answer/result that you say they are trying to give? in the experiment of the coin, we can arrange for the mutual agreement of the two approaches in every observable event (observable in the sense that it doesn't talk about probabilities)... for example, if you flip the coin and ask for the exact result it will give, both should agree in saying: "I can't tell"... if you say you flipped the coin a zillion times and aks for the proportion of heads, both should say immediately: "it's 1/2" (but they would interpret your question differently)... I guess you are talking about this difference: you ask what is the probability of you having a coin in your pocket. One bayesian could say: "I know nothing, so for me it is 1/2"... another bayesian could say: "I saw you handling coins before, and if I have a model for how probable it is for "coin handlers" to have coins in their pockets, I can update that probability of 1/2"... another bayesian could say: "I know that people in this city carry coins in their pockets with a chance of 30%, so it's 30%"... someone could say: "it is 80%, because I saw in the stars", but that wouldn't be bayesian, it's a personal kind of subjectivity... a frequentist would say: "i can't know, because I don't know anything related to the frequencies with which you carry coins in your pocket, i don't talk about probabilities for single events" now, those bayesians can't be right at the same time, yes? and that frequentist will take a long time to discover the frequency by making the situation become a repeatable experiment... the thing is, all bayesians are right, but their answers have limited power where the frequentist has no answers at all... it may seem silly, but that "imprecise" reasoning of bayesians has major applications, here's a very understandable example: en.wikipedia.org/wiki/Bayesian_search_theory
Bayesian and Frequentist are two thinking methods to answer different questions: what I know and what I should know. None are wrong, and it doesn't have to do with psychology or personality. It depends on the situation and which question should be answered first.
My interpretation is that the bayesian reasoning is correct, but the frequentist reasoning is easier for a variety of reasons so scientists often use it instead. I take this comment as empirical evidence for my claim, as the frequentist explanation takes about 1/3 of the words to explain than the bayesian.
49% heads. - 49% tails - 0.4% a bird steals it - 0.4% it disappears - 0.2% I’m imagining this and it doesn’t exist (but my eyes construct the visual spectrum in my mind)
As a psychiatrist, I feel like I rely on both Bayesian and Frequentist philosophies in my everyday work. When advising on diagnoses, I use the Bayesian approach. That is, I gather whatever data I can to inform an opinion (about a diagnosis), and then I update my opinion if and when more data emerges. I'm not overly invested in getting a 'right' diagnosis because a patient's presentation is dynamic and complex such that they can't always be reduced to a single category at all times. I'm happy to revise the diagnosis when necessary. But when I'm advising on risks (i.e. the risk of somebody committing suicide, homicide, arson, etc.), I use the Frequentist approach. I am infinitely more concerned about what will happen when a patient has had numerous repeated attempts at harming themselves or others because that informs the probability of how likely a person is going to repeat history. I think to myself, "what will happen if the patient attempts the same move another 100 times?" To me (and I'm not a statistician, although I know a little about human psychology), the Bayesian and Frequentist approaches are fundamentally concerned with certainty vs uncertainty. The Bayesian aligns herself with changeable opinions informed by available data, thus she is never completely 'certain' about anything since her opinions change when new data emerges. The Frequentist on the hand aligns himself with unchangeable facts based on logic, thus he is always completely 'certain' about everything as long as his logic holds water. The coin toss was a great teaching example. It was a great example because the answer was inconsequential. I mean... Who cares how the coin lands? Nobody was harmed in the making of the video, yes? (I hope). We can allow ourselves to assign equal weight to both philosophies in this teaching scenario when the outcome of the coin toss was inconsequential. I suspect people are likely to gravitate towards a Frequentist approach when contemplating decisions that are very consequential because the Frequentist approach feels more tangible to me while the Bayesian approach feels more abstract. So I don't think it is a matter of 'are you a Bayesian at heart or are you a Frequentist?' Rather, it may depend on the weight of the decision you are about to make. Having said that, I do acknowledge that some people are more tolerant of uncertainty than others, thus for those people, they are more likely to be Bayesian perhaps. Does this make sense?
It's less about the weight of the decision but the fundamental structure of the question. If you ask, "What is the probability I WILL flip a coin heads?" versus "What is the probability this is heads?" then this is the difference between the two thoughts and it doesn't matter the importance or the pertinence or the weight. So you are right in saying it has nothing to do with personality or thought process its just whether or not people are aware about the two different "modes" if you will of an outcome.
Do not mix human senses with the math. Both Bayesian and Frequentist approaches are mathematically solid and they converge when infinite data is available. F. put the uncertainty into sampling, i.e. we do not know the exact value because we only observe a limited subset of the universe and we can make an estimate of the interval where the true value can be. B. put the uncertainty in the value itself: as we have limited data available (including prior knowledge) we can say that the value in question can be drawn from a distribution. So instead of a point estimate B. give you a distribution of values. There is no more correct or less correct approach, it depends on what you want.
I like this approach! It definitely depends on how you want to model your problem, and, how you interpret the answer. Let's say your treatment is a parameter. The bayesian approach won't tell you what that parameter is, but will provide static confidence intervals of where it lies. More data, and informative priors will change the shape of this distribution. The frequentist approach will tell you the parameter (the treatment), with variable levels of confidence (depending on the data).
I am completely new to this concept but came down as a Bayesian thinker. I immediately thought however that my acceptance of uncertainty and willingness to make decisions even knowing the uncertainty is an unusual quality in me. It tends to drive others nuts as they prefer to be certain before acting. I guess I simply think certainty is an illusion most of the time. And I would definitely say that about medical risks as the research quality is often so poor or misunderstood or out of date and so on. Are you familiar with Ben Goldacre? If not please check his RUclips lectures.
I don't think the framing of Frequentists caring about the true answer is a good one. Bayesians and Frequentists both care about truth, they just care about the true answer to different questions. I think the main difference is that Bayesians and Frequentists ask different questions, and use language that implies the questions they care about, which is what makes it so difficult to have a conversation with the other perspective. When truly asking the same question, the two mindsets should converge on the same answer.
The main difference is how probability is defined. For Bayesians, probability is one's degree of belief. So, it is inherently subjective. For frequentists, probability is a law of the universe that regulates an event's long-term frequency of occuring. So, it's opposite of subjective. All the other differences stem from this one.
Very much agree. Wittgenstein would say: arguing for one, against the other, is simply an abuse of language. There is no contradiction. One is not right, while the other is wrong. Those that argue are misled by their own language use. Language is highly indeterminate. "What side is up?" Sounds like a simple and straightforward question, but it is not. It is based on context, the forms of life, and family resemblances. To the question, "what is the chance it is head's up?", it can be interpreted as in what is the chance your guess is correct, or what is the chance the actual state is head's up. In a deterministic universe, the frequentist would not even be able to say there is a 50% chance it lands head's up before the coin has landed. It may not have landed, but how it will land is determined by prior values that have already been set in motion.
I agree with banana's comment. For example when I read about zodiac signs, it usually describes the signs strengths and weaknesses. But I've always wondered how can someone who is not of that particular zodiac sign classify or identify a sign's attributes as a weakness? This assumption would imply that you've lived through their experiences.
If we say for Frequentists the probability of a system is a 'property of the Universe', a property of the system. Then Baysians allow talk about their belief of that probability, whereas Frequentists restrict themselves to estimates of the probability to calculations on the data. ?
I think it has a lot to do with the nature of the question and the search-space in your problem, rather than your personal choice, to go with a frequentist vs bayesian method.
@@cpmathews2566 You have no concept of the collective. As a collective it was what she said it was both for you and her because we all see the same colors on the rainbow. This schrodinger's cat thing is such a bas tardization of the scientific method and everything that has made progress in science up until that dumb concept came about. It's literally not true. The nature of statistics itself is that we can't determine something or its nature. Schrodinger took the nature of statistics itself and masked physical phenomenon with it and said "this is the fundamental nature of the universe" when the entire time it was relative to us and our ability to know. So statistics and its nature is schrodinger's cat we'll say but not the universe. You may be confused but the universe is certain.
I think it’s important to understand whether your need is action - doing or not doing something in the real world - or just thought/academic. Bayesian tends to promote action, such as our decision to drive more slowly in poor weather. Frequentist tends toward addressing issues where a discrete level of certainty has utility (often without action), such as hypothesis testing.
It seems like it first depends on how a person understands the initial question. I understood it as what's the probability of me guessing if it was heads or tails. Answer is always going to be 50/50. The coin already landed so it was never a question of which way it was resting on your palm. That has already been determined. The only thing left to do is guess the right answer...which is always going to be 50/50. Edit: This was such a random video click for me. Lol.
This is how I understood it as well. It seems kinda flawed, in a way. Is the way of determining whether you are Bayesian or Frequentist examining how you interpret implications in the question? As I stated in another reply, the question, as I believe is likely to be understood by most, would be "What is the probability [that you could correctly guess] that this coin is heads-up on my palm?" Or is the video saying that Bayensians would assume that she is referring to the guess and Frequentists won't? If that's the case, then Frequentists don't sound very fun at parties... I feel like this determines more about how wiling you are to "go along" with a potentially unclear question. I think, in a more casual setting, a Frequentist is still likely to guess 50% because, in their mind, they are going along with the commonly understood implication of the question, or, in other terms, "trying not to be a smart-ass." Is this psychology or statistics or both?
Thanks for summarizing this important topic. I've no emotional investment in the Frequentist vs Bayesian debate (I've used both often in my research), but I couldn't help but feel the Bayesian perspective was not given fair credit here. The Bayesian's "point of view" should not be entirely subjective, but rather based on logical principles, that can often be derived from the laws of nature (eg. The shape and symmetry of the coin make it equiprobable to land on heads or tails). The powerful advantage of leveraging prior information for forecasting or evaluating hypotheses also ought to be emphasized more. Ideally, aspects of both Bayes theorem and frequencies should be used (eg. using base rates as prior information in diagnostics). But because the frequentist approach is so much more intuitive to use in science, the Bayesian approach is underutilized. This has been less than optimal for science which has been far too dogmatic about p-values instead. It would be nice if you could emphasize this more in future communications on this topic, thanks!
This is a fantastic short explanation of the differences between them - thank you! Also, for some reason, you kind of remind me of Kes from Star Trek Voyager…
it occurs to me that most situations where you want to know a probability are Frequentist, i.e. they concern things that are already facts, but unknown to us. From a certain perspective *all* probabilities are Frequentist, if you accept that we live in a deterministic universe. All future tosses of the coin are already predetermined! Love this post!
The Baeysian recognizes that the probability is relative to perspective which means recognizing the context of other's perspevtive. Perspective must involve uncertainty. The problem is that it usually loses that component. I think some people combine the two to eliminate their feeling of discomfort.
If you can't provide an exact response, you're not interested in the truth. Frequentists can easily extrapolate based on past experiences while Bayesians would have a very hard time modeling those very same deterministic events. Let's say you succeed, and you manage to model every possibly deterministic event within your Bayesian model... Guess what, it's now a frequentist model!
I'm backing the superposition, where the superposition changes based on the likelihood that you were lying in the reveal, since the coin was too out of focus to tell what the result was.
Frequentist: "What is the probability the actual current state of the coin is ..."? Bayesian: "What is the probability my estimate of the state of the coin is ..."? It seems Frequentists try to take an objective point of view. Meaning: from the perspective of the focal object. Whereas the Bayesians take a subjective view. Meaning: from the perspective of the subject/observer.
The explanation of frequentist thinking in the video sits uneasily with me. The idea that a flipped, but hidden, coin would be either 0% or 100% (but unknown) while an unflipped coin would be 50%, or a coin flipped and waiting to land would be 50% seems arbitrary. It's more subjective than the Bayesian explanation in a way! There are a number of reasons why the outcome might be obscured to us, whether that data is temporally obscured (you have't flipped it yet, and we experience time in one direction!), or physically obscured (a hand is in the way), or obscured through laziness (the flipped coin is in the air waiting to land and we could measure the rotation and velocity and calculate how it will spin and drop and land, but we don't bother). I don't see, on an ideological level, why it should make a difference which of these it is. So if the hidden coin is "either 0% or 100% but I don't know which" to a frequentist, why not the future event coin too? It seems that there is something getting lost in the difference between the questions: "What side *will* this coin land?" and "What side *did* this coin land?" The frequentist as described here doesn't ever change their answer to the first question once the coin has flipped, they just start answering a different question instead, right? As I far off the mark if I were to think that maybe a change in information is being acknowledged in one case explicitly by changing the answer and in the other case implicitly by changing the question?
@@zak3744 You are correct in many things you say. In a deterministic view, everything is already determined. So, to a Frequentist this would have to mean that all coins being flipped, either in the future or past, all are determined ... and thus none have a probability. Only abstracted coins have probabilities in this sense. Elsewhere here, I commented about this being really a linguistic difference. The difference is not really about the understanding of reality, but what question is asked. Usually in science the Frequentist question tends to make most sense. It is about the object / objective reality. When you look at it from a decision making agent, it makes sense to look at it from a Bayesian perspective. The question is then about: what is my best estimate based on what I know? Or: the best decision based on the information available to the Agent (e.g., a robot).
Thank You.. You are a seriously great teacher, I'd like to see your videos as a necessary part of every high school students curriculum. You remove the jargon and re-frame the learning references to simple, understandable examples which makes the learning of complex issues so much easier.
Holy crap, statistics has a place for me. Never heard of Bayesian before. I gotta do some reading now. Thank you! Seriously, that makes so much sense in my world.
For that example I got Bayes. From my perspective, the coin is in an eternal state of 50/50. Until it is observed. Like quantum physics, What matters is the observation. Until I can see it, the coin is 50/50. I would say: it is just as likely to be heads up before or after the throw.
What if you make an x-ray and can see through the hand that it`s heads? Is the probability still 50/50 before you raise your hand and "see it" youth your own eyes?
@@thebrutaltooth1506 Assuming the x-ray is working correctly and it could show me that. *Yes* Because I observed it. In my opinion, an observation is any kind of measurement or reception of information through any way possible. e.g. tests, touch, etc. Evolutionary theory is based on this. We don't directly observe any of that information.
@@Lucas747G Interesting, I can respect that. Don`t know what you mean about the evolutionary theory though. You can directly observe evolution but by looking at the canges in a population not of an individual. "The English moth, Biston betularia, is a frequently cited example of observed evolution. In this moth there are two color morphs, light and dark (typica and carbonaria). H. Kettlewell found that dark moths constituted less than 2% of the population prior to 1848. Then, the frequency of the dark morph began to increase. By 1898, the 95% of the moths in Manchester and other highly industrialized areas were of the dark type, their frequency was less in rural areas. The moth population changed from mostly light colored moths to mostly dark colored moths. The moths' color was primarily determined by a single gene. So, the change in frequency of dark colored moths represented a change in the gene pool. This change was, by definition, evolution." (Source:abyss.uoregon.edu/~js/21st_century_science/lectures/lec09.html)
why is this a debate? if you have to make decisions with limited info, ie not knowing the data set (such as not having any more information prior to or after the coin flip) then you have to be Bayesian. If you know the data set, or if you're answering a silly question like "whats the probability that the coin has landed on the side that it has landed, no matter which one" then you have to be frequentist. If you wanna be technical, then frequentists have to be frequentists about all possibilities for every event, since given determinism all the coins HAVE in a sense, landed. But that's not useful from our perspective, so a lot of the time they have to be bayesian. I just don't see the debate, bayesianism and frequentism answer different questions, and which question is right to ask depends on the circumstance
Mathematically speaking (I am not a Mathematician, just a software developer), bayesians answers the question about the probability of the coin position based on given data, meaning "the coin has been thrown, and landed on either side" (it's important, since it could have landed vertically.. a very slight probability, but not really 0%... but since it has been stated it could only be heads or not, this possibility is discarded) "but since there is no actual data, and there are no more options, the probability is 50% for each one; Bayesian answers the question asked with the given data. Of course, similar to the Schrödinger's cat, there is no *certainty* about the results (although the coin's position IS determined, not a quantum state :-)), the Bayesian gives the most "reliable" answer: "50%". Obviously, if a person answers "0 or 100" it will be correct, but these are TWO answers, both have a 50% probability of being right, which is not what was asked: that the coin can be heads or tails IS THE PREMISE, so I could not use it as an ANSWER.Right...?
This is a finely done video - props to Kozyrkov for a superb presentation. I think, however, the emphasis on the subjectivity of Bayesian inference is a bit misleading. One comes away with the notion that frequentists are interested in reality while Bayesians are interested in opinions. Surely all practitioners of data-based inference are interested in reality; the difference lies in kinds of questions by which reality is sussed out. The Bayesian and the frequentist might agree that a given state or process in the world can be understood in terms of definite parameters, i.e. that the flipped coin has already landed. To say that the Bayesian approach is subjective is simply to say that it is concerned with *our knowledge* - or, equivalently, our *uncertainty* - regarding the parameters of interest given available evidence (data + priors). I suppose this could be called "subjective" since it depends on the knowledge available to a subject, but it is certainly not subjective in the pejorative sense of "arbitrary." In most cases, at least in my field of ecology, the frequentist is also interested in parameter states. That, after all, is what it means when we ask whether X causes Y. But frequentist methods get there indirectly by inferring the likelihood of evidence (data only, no priors) given assumed parameter states. While these approaches generate parameter estimates (parameter values that maximize the likellihood of the data) with uncertainty (intervals that would contain the true parameter value in X% of hypothetical repetitions of the sampling and analysis process), they do not tell us directly what we really want to know: what should we believe about the unknown state of the paramater? This is what we want to *know* because it guides what we want to *do*, i.e. to understand and potentially intervene in the world. These objectives, like our knowledge, are intrinsically subjective, but in a sense that is both legitimate and unavoidable. I also think it is a mistake - not one made explicitly by Kozyrkov, but one occasionally suggested by others - to project approaches to data-based inference onto metaphysics. Choosing between frequentist and Bayesian methodologies should have nothing to do with whether one is an ontological realist or nominalist. As Andrew Gelman puts it, "theoretical statistics is the theory of applies statistics." Pragmatic handling of uncertainty, appropriate to the question at hand, is the only end for which statistics is a legitimate means.
Cassie creates a nice discussion that is true in the narrow sense that it is possible to use the Bayesian paradigm to inject and update subjective points of view; however, this is an overly narrow reading. More broadly, Bayesian offers a mechanism to formulate a subjective coherent probability that is updated by evidence. We don't really know much about prior beliefs for parameters; perhaps, we only may say something about their support and the scale. So we posit weakly informative priors in a coherent way. The coherence comes from all quantities as measurable with respect to this probability model. Frequentism is often not coherent, but ad hoc. The p-value controversy is a good example of this. Of course, in the end, Bayesians are asked to demonstrate frequentist properties of their models, so frequentism is still the standard.
Is it possible to be a frequentist before the coin is flipped, like the answer of that coin landing heads or tails is already 100% or 0% which is predetermined by a multitude of factors such as its orientation at the moment, how hard you will flip it and so on, all of which are all also pre-determined but we just don’t know them
I kind of understand, a frequentist sounds like they care about what is "possible", if there are two possible options, like heads or tails and an event which has a before and an after. Before the event we can consider those 2 possibilities. After the event we can consider the outcome but there is no possibilities to consider, as one them was realised. If you have been taking prior beliefs and outcomes into account then you would have something to consider.
You didn't know what it was before you saw this video. So the probability was 50%. If you're a Frequentist. Now you can't make up your mind, so the probability is still 50%. If you are either. When you've made up your mind, but haven't told anyone, It's still 50%. But only if I'm a Bayesian. I have a pain between my ears.
But when we talk about Bayesians view, then one would need to mention Bayesian networks. And those shall rather be compared with the coin example. Because in Bayesian Nets you would actually construct a graph with a node saying "coin was flipped" and then dealing with the probability of the coin being flipped. That's were also the strengths of a BN approach lie. When you would need to narrow down in a (short) amount of events that certainly influence the outcome. So each approach heavly relies on the hypothesis to test. The more unknown factors you have the more you tend towards a frequentists view. Right?
01:00 Why did you look at the coin half-way through asking the question? The act of looking might change the results for some of the audience; so do they answer before you looked, or after you looked? The Bayesian probability of course changes for you; but to some extent changes for the audience, as they've see your reaction and thus received non-zero information about the true state of the coin.
My own research is in electronic engineering and I teach a graduate course on Stochastic Processes to engineers and applied mathematicians. I do research with both statisticians and other engineers, and have thus develop a rather pragmatic view. Losely, I pick the perspective which helps my current project. This leads me to be Bayesian 50 % of the time and frequentist 50 % of the time. (And Iannoy 100 % of the statisticians most of the time... ) I do not think that you should or need to choose between the two views. I think that both views are correct - but it is not the same thing they are looking at! That is probability to a Bayesian models the current uncertanty about an event whereas to a frequentist it models a frequency of correct guesses if the experiment could be repeated. Incidentially, the underlying probability theory (the events, probability measures and all that) applies to both schools. But although the terms (e.g. Probability, expectation, etc) used are interpreted in fundamentally different ways. Many times the two views can lead to the same thing. I pick the view which seems the most helpful in achieving my goal in a certain application. A perhaps even more fundamental concern to have, is the view on probability theory itself. The "Are real things random or not?" questions. As a pragmatic engineer, actually, I do not care - what matters to me is that probabilistic models, are very good and convenient models for many phenomena. Applying statistics be it frequentist or Bayesian, lead to many good ways of guessing on phenomena which cannot be observed directly.
"That is probability to a Bayesian models the current uncertanty about an event whereas to a frequentist it models a frequency of correct guesses if the experiment could be repeated." -- This feels like a more faithful representation of what's going on, to me.
@@6400ab wasn't it obvious what 'on' was used here for? Sit on the chair. Anyway, leave it. We are going into ambiguous linguistic terminology which is completely missing the point of this whole discussion.
what is the 'validity' of the question about probability of heads or tail once it is landed in your palm in this example is not clear ? what are its implications ?
Forgive my stupid question (which might be slightly off-topic), but doesn't it matter which side is facing up before the flip, how the coin is placed on the thumb, how much force it used for the flip, and some other factors (which may or may not be negligible)?
I don't know anything about statistics, but it sounds like when each group answers the "what probability is it that it's x?" question, they're focused on two different referents. The frequentists interpret the question as referring to the actual, determinate state of affairs in the world, while the Bayseians interpret it as an epistemological question, that is as a question about our knowledge. Two ways of interpreting what "probability" refers to.
this is exactly why I struggled so hard to grasp statistics, despite having no problem with advanced probability theory - I think in a Bayesian way, but my course in statistics was frequentist.
1:00 I thought it was a trick question and you were going to show the coin stading up, stuck between your fingers, to make a point about how there might not be a probability. Guess that makes me a Bayesian.
If the coin is heads-up before tossing, it will always land heads-up, and vice-versa, IF it's landing on the palm of the person tossing the coin. If it's landing on hard surface, it can go anywhere due to the bounce / twist / turn of the coin multiple times before it comes to rest. So, which one am I?
As a programmer, I kinda see both the same way. The Bayesian has a simplistic ideal model of the coin that they update. After 1000 tosses with 400 heads they may adjust their model to a 40% bias coin. The frequentist is looking for a different model. The perfect one that is deterministic, and predicts each toss. One is estimating the entropy of a sequence. The other is looking for the lowest entropy model that generates the sequence.
The way I thought of it was that the chance that an event did/can/will happen is actually always either 100% or 0% and it is just a lack of knowledge that makes it appear otherwise. Or in other words, probability is like a measurement of our own ignorance (are we slightly unsure or very unsure? etc). I don't know if that shit's true, it just looks like it to me.
Frequentism is realism about probabilities, Bayesianism is idealism about probabilities. Most scientists (still) are realists and this is why frequentism is the state of the art in statistical analysis and hypothesis testing. Recently various forms of anti-realism are being recognized not as a threat to science but as legitimate ways to address problems within science (e.g. constructive empiricism) and hence we'll see more Bayesian methods being applied. Machine learning is the most prominent field where this has already happened (and for good reasons - the things they're trying to build don't exist yet so there's nothing to discover about probabilities there, they have to be modeled).
I first answered 50%, then thought about it while she was peeking at the coin and said: 100%. Then thought about it a bit more and said: Meh, I have no idea. What does that make me?
Then you are an Bayesian. Why? A Frequenists would have answered "Frequenists" and then measure how often they were wrong. You want to guess right and therefore say both (just like a Bayesian does with the coin)
What's the frequentist perspective on getting the model right? It always seemed to be like bayseans try to make that more explicit but I struggle to see a real distinction, but I'm kind of convinced (after adjusting my prior ;-) I just don't understand the semantic distinction that the frequentist perspective had with respect to (implicit) assumptions
Thank you for the simple explanation :) As far as I understand, the frequentist statistics is correct. However, from my point of view as a research scientist, the frequentist statistics is often irrelevant! Because I am often interested to know if my model or explanation of a complicated reality is consistent with the observations. These types of questions are consistently addressed within the framework of Bayesian statistics. On the other hand, the Bayesian approach is still missing an important ingredient. Bayesians still do not agree on how to construct priors! How does one construct a prior, which represents one's knowledge?
just came across this wonderful video, very simple explanation, read many articles but still confuse with the technical terminologies they have used in the paper. from this video within 5 minutes i have understood the concept. Thankyou Cassie for sharing wonderful knowledge with us. really appreciate it :)
If you have not yet seen the coin, according to your description, the frequentist would have to say 50%, because that's the probability they would guess correctly if they had to guess heads or tails. But that's the Bayesian approach. The Bayesian is in the subjective position to guess. The frequentist does not guess, he is concerned about the global asymptotic frequency. And the Bayesian does have a way to determine how well his assumptions were, the level of surprise. Given his assumptions, how likely or unlikely was the observation, how much did he need to change his prior beliefs.
In my undergraduate statistics courses, I essentially was indoctrinated to think in a frequentist way, to look for the result of a statistical experiment and say that I conclude with 95% confidence (or based on whatever your confidence level was) that a result was significant, or say that I have failed to reject the null hypothesis. So far, I still like that way of thinking.
Hm, I'm wondering whether I can say this?: 1) Frequentist statistic is an inductive approach - trying to infer properties of the population from collected data (which also includes evaluating the assumptions of properties of the population by analysing the likelihoods of data given these assumptions --> see significance testing). 2) Probability is deductive - "knowing" properties of the population and inferring properties (probabilities) of data points from that. (And Bayes specifically includes Beliefs, which can be updated). P.S. I'm not sure how to handle the concepts probability and Bayes - are they the same or is Bayes a special case of probability or ...?
This video... is the best thing about COVID-19. I was hoping the world would start to get science more, but looking around, no, no. This video on the other hand, while it does not even mention Sars2, ticks the box. Proceed.
So, if I was to try and put that in terms I’ve spent some time with, I’d say: A Bayesian attempt at ‘finding truth in uncertainty’/‘making predictions’ finds base rates relevant. So we cultivate relevance around the coin only landing on heads or tails, but do not place relevance on the physics of the coins’ trajectory and inertia, physical determinence, interaction with air molecules, etc etc. We use base rates as an end, and not a means to an end. A Frequentist will cultivate relevance of those latter things, as they claim we shall assert we live in a determined universe, but in so far as we cannot fully gasp all the elements of that determination, we can use statistical models instead and judge their efficacy from the outcomes. Is that right?
The chance of a coin landing heads/tails is always 50%. The current state of a coin is determined, which is a different question, despite it being hidden, there is a definitive state. The definitive state is that it is 100% side A or 0% side A, p(side A) = 50% still.
It's curious to think about probability and statistics theories in physics. In my perspective, the experimental physicists generally goes with a Frequentist mind, since the common mindset is to try the same experiment over and over and look what percentage they got a "good answer". In the other hand , the theorists care too much about perspective and information, actually the quantum theory is bounded to theses concepts, hence, the resolutions of the problems are made from a Bayesian mind. Your videos are awesome! Loved it!
I said 40 percent based upon the fact she had a hand that caught the coin at a non level planar and that the coin may be weighted slightly more on one side due to grime build up
please explain: so, from a bayesian perspective, yes the coin has already landed, but the core of the question is what was the probability of it having landed on heads or tails? it can only ever be one of two twings, yes or no, blue or red, up or down, always 50% to be or not to be.
As a kid, I used to wonder what the space between the stove and the pot was called. As an adult, I had the same issue with frequentism, I just didn't know how to formulate the question.
actually at the end of Bayesian statistics it goes back to Frequentist style for example Gibbs Sampling, posterior predictive check it needs a lost of sample which come from its own distribution that s why it calls generative in machine learning
There is no such thing as rigid distinction between the two, I use both, just not for the same reasons obviously. Why would you choose only one anyway? There isn't a better one, so don't choose, both are important, and both can be very useful to consider in a same situation to see different things, it helps resolve problems in (unusual sometimes but) effective ways. I'm just gonna leave it here but if rings any bell to somebody: I try to never be content with my deductions or ways of seeing and conceiving things, so I try to force myself to see from perspectives where I'm always wrong, even if it's from stupid reasoning/perspectives, it helps see unexpected things and patterns sometimes where we expect them the least and it drastically help understanding notions of relativity.
Interesting. I think what I am seeing here is that Frequentists must turn into Bayesians if they wish to use statistical methods to determine the likelihood of a system being in a specific state in the future relative to another possible state. For example, the probability of precipitation, simply because the Frequentists have to wait for the forecast valid time to arrive in order to have any chance (pardon the pun) to make their assessment.
Cassie, thank you for detailed explanation. Please, please, please tell us more about pros and cons of Bayesian vs Frequentist approaches in the business context.
Statistical probability is a measure of ignorance, not certainty. Everything that Does happen always had a 100% chance of happening, we just didn't have enough information to know it. The two perspectives are perfectly compatible. Also, knowledge is justified belief.
Agree on the first bit, but not on the second. Knowledge is not simply justified belief, some does occur that way but much is also direct knowledge that does not require a belief.
So, is there a problem in statistical analysis where a Bayesian and a Frequentist would come up with different, empirically distinguishable answers? And if so, which answer would turn out to be correct?
It's important to note that frequentist theory is an incomplete theory. Bayesian inference is a theory that represents reality better -- with more accuracy. It addresses uncertainty, for any state of knowledge. It's also important to note that frequentists try to estimate a parameter (point/range estimate) for something. Bayesians try to evaluate degrees of plausibilities among hypotheses for a specific parameter. These are two different approaches to the problem of trying to figure out what the parameter is. Therefore the interpretations of them are also different!
The problem with this test is that it has no implication. The person on the other side of the table forms opinion but does he act differently? With your coin-tossing example if there are one Baysian and one Frequentist on the other side of the table and they want to engage with you in a game of chance are they going to bet differently on a coin that you have already tossed? A better example would be for you to toss a coin once and show the income to One Baysian and One Frequentis. The outcome is Head. Then you ask them to bet on the next income to be Head. What odds the Baysian and Frequentis would agree to?
Observational data. It is always full of known and unknown biases and confounding effects. Different people will have different opinions as to the sources and magnitudes of these effects. It is unreasonable to use frequentist statistics in these cases. Where there is a formal experimental process (e.g. randomised controlled trials) then frequentist approaches are the way to go. The overall process is focussed around finding the truth (as far as possible). The problem arises in applying frequentist approaches to observational data and then saying 'this is the truth'. There is a lot more observational data then that from formal experiments, leading to a temptation to apply frequentist statistics where they are inappropriate. Where there is only observational data we have many different opinions and in a scientific age that feels unsatisfactory - but that is just the way things are.
Watched this a few more times. As far as this example therein, the frequentist is orientated around what the truth of the outcome has been probabilistically. Initially past tense thinking, maybe past will become prologue, maybe it can't or won't. And the Bayesian may not care so much about whether the outcome should or should not be classified probabilistically in any technical sense, as the value of such a pursuit thereof is taken for granted by sheer fact of the problem being analyzed, short of any shenanigans, or accompanying thought experiments, as a natural extension of the input state, considerations toward and about the conditions and processes involved with how the outcome may likely come to fruition, or in a word or three, the driving phenomena methods pertaining to the event under consideration, and what's to follow upon the onset of the coin being flipped, etc,...blam outcome, assessment anew, etc. -- Whereas, frequentism lends itself to be willing to trade knowing the why of coin flipping, for any value that may come with being able to _efficiently_ analyze flipped coin outcomes' probability calculation(s) thereto.
@@dgodiex of course it's on point. 90% of what is put out by any entity with massive reach is to manipulate opinions. what the fuck is the point of pushing a psychology video to BILLIONS whose only real message is YOURE ALL DIFFERENT AND NOW GO THINK ABOUT IT? She keeps hinting at "what is right? what's more logical? EHHH..." and she leaves it open for people to start mentally pointing fingers. she's egging you on, begging you to judge them. its such bullshit and MATTERS 0%.
If it's philosophical, I'm surprised that the simple premise that 'Switching out of the default answer' as a question is by itself deviating out of the default... i.e. if I brush my teeth everyday the past week as it is my defaulted decision at the start of the week, but next week, everytime I brush, if I choose to contemplate if or not to brush before I do it... it's already not default... Hence Bayesian and Frequentist is simply what I would call a difference between '0 and 1' and '-1 and 1' when taking decisions... it doesn't matter how you encode your decisions... you could choose not to do it.. or you could choose to not do it... doesn't make a literal difference, only makes a difference in framing of your decision in manners where you consider inaction as action
I believe I cannot love this video enough. I've watched it over and over and recommended it to many people. But then again this is just my belief which I'm willing to change in the future based on the data. I believe this makes me biased towards being a Bayesian, but someone correct me if I'm wrong. 😇
Clear explanation, thanks. Will it be possible to have a mathematical explanation as well, such as doing the same analysis (for instance comparing mean across two groups) using Frequentist (a t-test) versus Bayesian approach (?) ?
I love this subject! I'm studying Bayesian methods in my PhD, here's my perspective:
Frequentist reasoning wants to deal objectively with data, so it considers probability to be a property of the world; it says "the coin has probability 1/2 of being heads because that's the frequency of heads in the behavior of this coin"... and there's a right probability, it's a fact from the world, it can be learned by data that shows that frequency in behavior. Data is noisy, but it reveals true propensities through frequencies.
Bayesian reasoning wants to deal logically with data, so it considers probability to be a property of logical propositions about the world; it says "the statement 'coin landed heads' has a certain probability of being true, it is 1/2 for me and 0 or 1 for you depending on what you see"... the proposition is connected to a point of view, and different points of view will differ in how close they are to the truth about the state of the coin. So probability is subjective in a sense, but all points of view with equal information should objectively agree about probabilities of their statements (it's objectively subjective, just recognizing the existence of different points of view, but they are not supposed to be personal, not opinions). When you update your "belief" over data, it's because data moved your point of view in relation to the "truth". In this example, once we see the coin, we update the statement "coin landed heads" from 1/2 to 0 or 1 depending on what we see (probabilities of 0 and 1 mean perfect information while 1/2 means no information).
There isn't an actual divide between the two, theoretically... Bayesian reasoning recognizes the relation between frequency and plausibility, while frequentist reasoning recognizes points of view, it just doesn't go there.
So in other words the frequentists approach will give you a correct answer every time but may need indefinitely to evaluate, while the bayesian approach gives you a result immediately but this result may be wrong.
@@ndrsvgl hm... the approaches are answering different questions, both correctly... what is this answer/result that you say they are trying to give?
in the experiment of the coin, we can arrange for the mutual agreement of the two approaches in every observable event (observable in the sense that it doesn't talk about probabilities)... for example, if you flip the coin and ask for the exact result it will give, both should agree in saying: "I can't tell"... if you say you flipped the coin a zillion times and aks for the proportion of heads, both should say immediately: "it's 1/2" (but they would interpret your question differently)...
I guess you are talking about this difference: you ask what is the probability of you having a coin in your pocket. One bayesian could say: "I know nothing, so for me it is 1/2"... another bayesian could say: "I saw you handling coins before, and if I have a model for how probable it is for "coin handlers" to have coins in their pockets, I can update that probability of 1/2"... another bayesian could say: "I know that people in this city carry coins in their pockets with a chance of 30%, so it's 30%"... someone could say: "it is 80%, because I saw in the stars", but that wouldn't be bayesian, it's a personal kind of subjectivity... a frequentist would say: "i can't know, because I don't know anything related to the frequencies with which you carry coins in your pocket, i don't talk about probabilities for single events"
now, those bayesians can't be right at the same time, yes? and that frequentist will take a long time to discover the frequency by making the situation become a repeatable experiment... the thing is, all bayesians are right, but their answers have limited power where the frequentist has no answers at all... it may seem silly, but that "imprecise" reasoning of bayesians has major applications, here's a very understandable example: en.wikipedia.org/wiki/Bayesian_search_theory
Bayesian and Frequentist are two thinking methods to answer different questions: what I know and what I should know. None are wrong, and it doesn't have to do with psychology or personality. It depends on the situation and which question should be answered first.
@@lrgui9792@N73B60 Ok, thanks for clarification.
My interpretation is that the bayesian reasoning is correct, but the frequentist reasoning is easier for a variety of reasons so scientists often use it instead. I take this comment as empirical evidence for my claim, as the frequentist explanation takes about 1/3 of the words to explain than the bayesian.
49% heads. - 49% tails - 0.4% a bird steals it - 0.4% it disappears - 0.2% I’m imagining this and it doesn’t exist (but my eyes construct the visual spectrum in my mind)
As a psychiatrist, I feel like I rely on both Bayesian and Frequentist philosophies in my everyday work. When advising on diagnoses, I use the Bayesian approach. That is, I gather whatever data I can to inform an opinion (about a diagnosis), and then I update my opinion if and when more data emerges. I'm not overly invested in getting a 'right' diagnosis because a patient's presentation is dynamic and complex such that they can't always be reduced to a single category at all times. I'm happy to revise the diagnosis when necessary.
But when I'm advising on risks (i.e. the risk of somebody committing suicide, homicide, arson, etc.), I use the Frequentist approach. I am infinitely more concerned about what will happen when a patient has had numerous repeated attempts at harming themselves or others because that informs the probability of how likely a person is going to repeat history. I think to myself, "what will happen if the patient attempts the same move another 100 times?"
To me (and I'm not a statistician, although I know a little about human psychology), the Bayesian and Frequentist approaches are fundamentally concerned with certainty vs uncertainty. The Bayesian aligns herself with changeable opinions informed by available data, thus she is never completely 'certain' about anything since her opinions change when new data emerges. The Frequentist on the hand aligns himself with unchangeable facts based on logic, thus he is always completely 'certain' about everything as long as his logic holds water.
The coin toss was a great teaching example. It was a great example because the answer was inconsequential. I mean... Who cares how the coin lands? Nobody was harmed in the making of the video, yes? (I hope). We can allow ourselves to assign equal weight to both philosophies in this teaching scenario when the outcome of the coin toss was inconsequential.
I suspect people are likely to gravitate towards a Frequentist approach when contemplating decisions that are very consequential because the Frequentist approach feels more tangible to me while the Bayesian approach feels more abstract.
So I don't think it is a matter of 'are you a Bayesian at heart or are you a Frequentist?' Rather, it may depend on the weight of the decision you are about to make. Having said that, I do acknowledge that some people are more tolerant of uncertainty than others, thus for those people, they are more likely to be Bayesian perhaps.
Does this make sense?
It's less about the weight of the decision but the fundamental structure of the question. If you ask, "What is the probability I WILL flip a coin heads?" versus "What is the probability this is heads?" then this is the difference between the two thoughts and it doesn't matter the importance or the pertinence or the weight. So you are right in saying it has nothing to do with personality or thought process its just whether or not people are aware about the two different "modes" if you will of an outcome.
Do not mix human senses with the math. Both Bayesian and Frequentist approaches are mathematically solid and they converge when infinite data is available. F. put the uncertainty into sampling, i.e. we do not know the exact value because we only observe a limited subset of the universe and we can make an estimate of the interval where the true value can be. B. put the uncertainty in the value itself: as we have limited data available (including prior knowledge) we can say that the value in question can be drawn from a distribution. So instead of a point estimate B. give you a distribution of values. There is no more correct or less correct approach, it depends on what you want.
I like this approach! It definitely depends on how you want to model your problem, and, how you interpret the answer. Let's say your treatment is a parameter. The bayesian approach won't tell you what that parameter is, but will provide static confidence intervals of where it lies. More data, and informative priors will change the shape of this distribution. The frequentist approach will tell you the parameter (the treatment), with variable levels of confidence (depending on the data).
I am completely new to this concept but came down as a Bayesian thinker. I immediately thought however that my acceptance of uncertainty and willingness to make decisions even knowing the uncertainty is an unusual quality in me. It tends to drive others nuts as they prefer to be certain before acting. I guess I simply think certainty is an illusion most of the time. And I would definitely say that about medical risks as the research quality is often so poor or misunderstood or out of date and so on. Are you familiar with Ben Goldacre? If not please check his RUclips lectures.
Psychiatry is GAY.
I don't think the framing of Frequentists caring about the true answer is a good one. Bayesians and Frequentists both care about truth, they just care about the true answer to different questions.
I think the main difference is that Bayesians and Frequentists ask different questions, and use language that implies the questions they care about, which is what makes it so difficult to have a conversation with the other perspective. When truly asking the same question, the two mindsets should converge on the same answer.
The main difference is how probability is defined. For Bayesians, probability is one's degree of belief. So, it is inherently subjective. For frequentists, probability is a law of the universe that regulates an event's long-term frequency of occuring. So, it's opposite of subjective. All the other differences stem from this one.
Very much agree. Wittgenstein would say: arguing for one, against the other, is simply an abuse of language. There is no contradiction. One is not right, while the other is wrong. Those that argue are misled by their own language use. Language is highly indeterminate. "What side is up?" Sounds like a simple and straightforward question, but it is not. It is based on context, the forms of life, and family resemblances. To the question, "what is the chance it is head's up?", it can be interpreted as in what is the chance your guess is correct, or what is the chance the actual state is head's up.
In a deterministic universe, the frequentist would not even be able to say there is a 50% chance it lands head's up before the coin has landed. It may not have landed, but how it will land is determined by prior values that have already been set in motion.
I agree with banana's comment. For example when I read about zodiac signs, it usually describes the signs strengths and weaknesses.
But I've always wondered how can someone who is not of that particular zodiac sign classify or identify a sign's attributes as a weakness? This assumption would imply that you've lived through their experiences.
P.S. they're trying to raise robots. I think it's in a Disney movie "Inside Out"
If we say for Frequentists the probability of a system is a 'property of the Universe', a property of the system. Then Baysians allow talk about their belief of that probability, whereas Frequentists restrict themselves to estimates of the probability to calculations on the data. ?
I think it has a lot to do with the nature of the question and the search-space in your problem, rather than your personal choice, to go with a frequentist vs bayesian method.
Exactly
LOL. Schroedinger's coin.
Not only Schrödinger's coin, at 50/50; But when she showed us the coin I could not see it clearly. For me it is still, 50/50. Fore her it's 100%
@@cpmathews2566 You have no concept of the collective. As a collective it was what she said it was both for you and her because we all see the same colors on the rainbow. This schrodinger's cat thing is such a bas tardization of the scientific method and everything that has made progress in science up until that dumb concept came about. It's literally not true. The nature of statistics itself is that we can't determine something or its nature. Schrodinger took the nature of statistics itself and masked physical phenomenon with it and said "this is the fundamental nature of the universe" when the entire time it was relative to us and our ability to know. So statistics and its nature is schrodinger's cat we'll say but not the universe. You may be confused but the universe is certain.
@@traininggrounds9450 relax. quantum bayesianism is a thing. just has its own limitations with locality etc etc.
Hilarious
What is the chances the coin is not there in her hand ?
I think it’s important to understand whether your need is action - doing or not doing something in the real world - or just thought/academic. Bayesian tends to promote action, such as our decision to drive more slowly in poor weather. Frequentist tends toward addressing issues where a discrete level of certainty has utility (often without action), such as hypothesis testing.
Your action vs action recommended as an expert interpreting data?
It seems like it first depends on how a person understands the initial question. I understood it as what's the probability of me guessing if it was heads or tails. Answer is always going to be 50/50. The coin already landed so it was never a question of which way it was resting on your palm. That has already been determined. The only thing left to do is guess the right answer...which is always going to be 50/50.
Edit: This was such a random video click for me. Lol.
This is how I understood it as well. It seems kinda flawed, in a way. Is the way of determining whether you are Bayesian or Frequentist examining how you interpret implications in the question? As I stated in another reply, the question, as I believe is likely to be understood by most, would be "What is the probability [that you could correctly guess] that this coin is heads-up on my palm?" Or is the video saying that Bayensians would assume that she is referring to the guess and Frequentists won't? If that's the case, then Frequentists don't sound very fun at parties...
I feel like this determines more about how wiling you are to "go along" with a potentially unclear question. I think, in a more casual setting, a Frequentist is still likely to guess 50% because, in their mind, they are going along with the commonly understood implication of the question, or, in other terms, "trying not to be a smart-ass."
Is this psychology or statistics or both?
I agree. I had to watch it again because it made no sense to me! Her metaphor / analogy / example is poor.
Thanks for summarizing this important topic. I've no emotional investment in the Frequentist vs Bayesian debate (I've used both often in my research), but I couldn't help but feel the Bayesian perspective was not given fair credit here. The Bayesian's "point of view" should not be entirely subjective, but rather based on logical principles, that can often be derived from the laws of nature (eg. The shape and symmetry of the coin make it equiprobable to land on heads or tails). The powerful advantage of leveraging prior information for forecasting or evaluating hypotheses also ought to be emphasized more. Ideally, aspects of both Bayes theorem and frequencies should be used (eg. using base rates as prior information in diagnostics). But because the frequentist approach is so much more intuitive to use in science, the Bayesian approach is underutilized. This has been less than optimal for science which has been far too dogmatic about p-values instead. It would be nice if you could emphasize this more in future communications on this topic, thanks!
Two minutes in to my first Cassie Kozyrkov video and I'm subscribed.
Me too!
Thank you. Perfect pausing during the presentation. It is so rare among RUclips presenters.
*Neo* "Heads!"
*Morpheus* - "What if I told you there was no coin...?"
Hidden under your other hand or hidden in the future, is there a meaningful difference?
This is a fantastic short explanation of the differences between them - thank you!
Also, for some reason, you kind of remind me of Kes from Star Trek Voyager…
Great video! What are you recovering from as a statistician?
it occurs to me that most situations where you want to know a probability are Frequentist, i.e. they concern things that are already facts, but unknown to us. From a certain perspective *all* probabilities are Frequentist, if you accept that we live in a deterministic universe. All future tosses of the coin are already predetermined!
Love this post!
The Baeysian recognizes that the probability is relative to perspective which means recognizing the context of other's perspevtive. Perspective must involve uncertainty. The problem is that it usually loses that component. I think some people combine the two to eliminate their feeling of discomfort.
And the Micheal Baysians don’t care I’d it’s heads or tails, as long as the camera orbits it.
And as long as there are pyrotechnics and explosions.
“The truth has already been fixed in the universe”.
Powerful, powerful stuff. 🙏
A better question is, would you go for Monte Carlo simulations or bootstrap draws for small samples 😉
and what if I do both?
If you can't provide an exact response, you're not interested in the truth. Frequentists can easily extrapolate based on past experiences while Bayesians would have a very hard time modeling those very same deterministic events. Let's say you succeed, and you manage to model every possibly deterministic event within your Bayesian model... Guess what, it's now a frequentist model!
Hands down the best video I’ve watched on the philosophy behind both the Bayesian and Frequentist approach. Well done
I'm backing the superposition, where the superposition changes based on the likelihood that you were lying in the reveal, since the coin was too out of focus to tell what the result was.
I can't believe that we are the only two people who have figured this out.
Frequentist: "What is the probability the actual current state of the coin is ..."?
Bayesian: "What is the probability my estimate of the state of the coin is ..."?
It seems Frequentists try to take an objective point of view. Meaning: from the perspective of the focal object. Whereas the Bayesians take a subjective view. Meaning: from the perspective of the subject/observer.
I like that description more than her use of the word "opinion".
The explanation of frequentist thinking in the video sits uneasily with me. The idea that a flipped, but hidden, coin would be either 0% or 100% (but unknown) while an unflipped coin would be 50%, or a coin flipped and waiting to land would be 50% seems arbitrary. It's more subjective than the Bayesian explanation in a way! There are a number of reasons why the outcome might be obscured to us, whether that data is temporally obscured (you have't flipped it yet, and we experience time in one direction!), or physically obscured (a hand is in the way), or obscured through laziness (the flipped coin is in the air waiting to land and we could measure the rotation and velocity and calculate how it will spin and drop and land, but we don't bother). I don't see, on an ideological level, why it should make a difference which of these it is. So if the hidden coin is "either 0% or 100% but I don't know which" to a frequentist, why not the future event coin too?
It seems that there is something getting lost in the difference between the questions: "What side *will* this coin land?" and "What side *did* this coin land?" The frequentist as described here doesn't ever change their answer to the first question once the coin has flipped, they just start answering a different question instead, right? As I far off the mark if I were to think that maybe a change in information is being acknowledged in one case explicitly by changing the answer and in the other case implicitly by changing the question?
@@zak3744 You are correct in many things you say. In a deterministic view, everything is already determined. So, to a Frequentist this would have to mean that all coins being flipped, either in the future or past, all are determined ... and thus none have a probability. Only abstracted coins have probabilities in this sense.
Elsewhere here, I commented about this being really a linguistic difference. The difference is not really about the understanding of reality, but what question is asked.
Usually in science the Frequentist question tends to make most sense. It is about the object / objective reality. When you look at it from a decision making agent, it makes sense to look at it from a Bayesian perspective. The question is then about: what is my best estimate based on what I know? Or: the best decision based on the information available to the Agent (e.g., a robot).
Thank You.. You are a seriously great teacher, I'd like to see your videos as a necessary part of every high school students curriculum. You remove the jargon and re-frame the learning references to simple, understandable examples which makes the learning of complex issues so much easier.
Holy crap, statistics has a place for me. Never heard of Bayesian before. I gotta do some reading now. Thank you! Seriously, that makes so much sense in my world.
This video, besides sprouting an interest in the philosophy of probability (to put it lightly) and how English sounds to those who don't speak it.
For that example I got Bayes. From my perspective, the coin is in an eternal state of 50/50. Until it is observed. Like quantum physics, What matters is the observation. Until I can see it, the coin is 50/50. I would say: it is just as likely to be heads up before or after the throw.
What if you make an x-ray and can see through the hand that it`s heads? Is the probability still 50/50 before you raise your hand and "see it" youth your own eyes?
@@thebrutaltooth1506 Assuming the x-ray is working correctly and it could show me that. *Yes* Because I observed it. In my opinion, an observation is any kind of measurement or reception of information through any way possible. e.g. tests, touch, etc. Evolutionary theory is based on this. We don't directly observe any of that information.
@@Lucas747G Interesting, I can respect that. Don`t know what you mean about the evolutionary theory though. You can directly observe evolution but by looking at the canges in a population not of an individual.
"The English moth, Biston betularia, is a frequently cited example of observed evolution. In this moth there are two color morphs, light and dark (typica and carbonaria). H. Kettlewell found that dark moths constituted less than 2% of the population prior to 1848. Then, the frequency of the dark morph began to increase. By 1898, the 95% of the moths in Manchester and other highly industrialized areas were of the dark type, their frequency was less in rural areas. The moth population changed from mostly light colored moths to mostly dark colored moths. The moths' color was primarily determined by a single gene. So, the change in frequency of dark colored moths represented a change in the gene pool. This change was, by definition, evolution." (Source:abyss.uoregon.edu/~js/21st_century_science/lectures/lec09.html)
The Bayesian perspective reminds me very much of Schrödinger's cat experiment. :-)
why is this a debate? if you have to make decisions with limited info, ie not knowing the data set (such as not having any more information prior to or after the coin flip) then you have to be Bayesian. If you know the data set, or if you're answering a silly question like "whats the probability that the coin has landed on the side that it has landed, no matter which one" then you have to be frequentist. If you wanna be technical, then frequentists have to be frequentists about all possibilities for every event, since given determinism all the coins HAVE in a sense, landed. But that's not useful from our perspective, so a lot of the time they have to be bayesian. I just don't see the debate, bayesianism and frequentism answer different questions, and which question is right to ask depends on the circumstance
Mathematically speaking (I am not a Mathematician, just a software developer), bayesians answers the question about the probability of the coin position based on given data, meaning "the coin has been thrown, and landed on either side" (it's important, since it could have landed vertically.. a very slight probability, but not really 0%... but since it has been stated it could only be heads or not, this possibility is discarded) "but since there is no actual data, and there are no more options, the probability is 50% for each one; Bayesian answers the question asked with the given data. Of course, similar to the Schrödinger's cat, there is no *certainty* about the results (although the coin's position IS determined, not a quantum state :-)), the Bayesian gives the most "reliable" answer: "50%". Obviously, if a person answers "0 or 100" it will be correct, but these are TWO answers, both have a 50% probability of being right, which is not what was asked: that the coin can be heads or tails IS THE PREMISE, so I could not use it as an ANSWER.Right...?
This is why I’ll never understand statistics beyond mean and standard deviation.
This is a finely done video - props to Kozyrkov for a superb presentation.
I think, however, the emphasis on the subjectivity of Bayesian inference is a bit misleading. One comes away with the notion that frequentists are interested in reality while Bayesians are interested in opinions. Surely all practitioners of data-based inference are interested in reality; the difference lies in kinds of questions by which reality is sussed out.
The Bayesian and the frequentist might agree that a given state or process in the world can be understood in terms of definite parameters, i.e. that the flipped coin has already landed. To say that the Bayesian approach is subjective is simply to say that it is concerned with *our knowledge* - or, equivalently, our *uncertainty* - regarding the parameters of interest given available evidence (data + priors). I suppose this could be called "subjective" since it depends on the knowledge available to a subject, but it is certainly not subjective in the pejorative sense of "arbitrary."
In most cases, at least in my field of ecology, the frequentist is also interested in parameter states. That, after all, is what it means when we ask whether X causes Y. But frequentist methods get there indirectly by inferring the likelihood of evidence (data only, no priors) given assumed parameter states. While these approaches generate parameter estimates (parameter values that maximize the likellihood of the data) with uncertainty (intervals that would contain the true parameter value in X% of hypothetical repetitions of the sampling and analysis process), they do not tell us directly what we really want to know: what should we believe about the unknown state of the paramater? This is what we want to *know* because it guides what we want to *do*, i.e. to understand and potentially intervene in the world. These objectives, like our knowledge, are intrinsically subjective, but in a sense that is both legitimate and unavoidable.
I also think it is a mistake - not one made explicitly by Kozyrkov, but one occasionally suggested by others - to project approaches to data-based inference onto metaphysics. Choosing between frequentist and Bayesian methodologies should have nothing to do with whether one is an ontological realist or nominalist. As Andrew Gelman puts it, "theoretical statistics is the theory of applies statistics." Pragmatic handling of uncertainty, appropriate to the question at hand, is the only end for which statistics is a legitimate means.
I think it all depends on which hand you catch it in and which hand is over the coin and which hand is under.
Cassie creates a nice discussion that is true in the narrow sense that it is possible to use the Bayesian paradigm to inject and update subjective points of view; however, this is an overly narrow reading. More broadly, Bayesian offers a mechanism to formulate a subjective coherent probability that is updated by evidence. We don't really know much about prior beliefs for parameters; perhaps, we only may say something about their support and the scale. So we posit weakly informative priors in a coherent way. The coherence comes from all quantities as measurable with respect to this probability model. Frequentism is often not coherent, but ad hoc. The p-value controversy is a good example of this. Of course, in the end, Bayesians are asked to demonstrate frequentist properties of their models, so frequentism is still the standard.
Is it possible to be a frequentist before the coin is flipped, like the answer of that coin landing heads or tails is already 100% or 0% which is predetermined by a multitude of factors such as its orientation at the moment, how hard you will flip it and so on, all of which are all also pre-determined but we just don’t know them
I recommend reading the short paper Bayesian Estimation Supersedes the t Test.
I kind of understand, a frequentist sounds like they care about what is "possible", if there are two possible options, like heads or tails and an event which has a before and an after.
Before the event we can consider those 2 possibilities.
After the event we can consider the outcome but there is no possibilities to consider, as one them was realised.
If you have been taking prior beliefs and outcomes into account then you would have something to consider.
Interesting paradox (?) I just came across:
The probability that I'm a Frequentist is 50%.
so you are bayesian 100%
You didn't know what it was before you saw this video. So the probability was 50%. If you're a Frequentist.
Now you can't make up your mind, so the probability is still 50%. If you are either.
When you've made up your mind, but haven't told anyone, It's still 50%. But only if I'm a Bayesian.
I have a pain between my ears.
But when we talk about Bayesians view, then one would need to mention Bayesian networks. And those shall rather be compared with the coin example. Because in Bayesian Nets you would actually construct a graph with a node saying "coin was flipped" and then dealing with the probability of the coin being flipped. That's were also the strengths of a BN approach lie. When you would need to narrow down in a (short) amount of events that certainly influence the outcome. So each approach heavly relies on the hypothesis to test. The more unknown factors you have the more you tend towards a frequentists view. Right?
01:00 Why did you look at the coin half-way through asking the question?
The act of looking might change the results for some of the audience; so do they answer before you looked, or after you looked? The Bayesian probability of course changes for you; but to some extent changes for the audience, as they've see your reaction and thus received non-zero information about the true state of the coin.
My own research is in electronic engineering and I teach a graduate course on Stochastic Processes to engineers and applied mathematicians. I do research with both statisticians and other engineers, and have thus develop a rather pragmatic view. Losely, I pick the perspective which helps my current project. This leads me to be Bayesian 50 % of the time and frequentist 50 % of the time. (And Iannoy 100 % of the statisticians most of the time... ) I do not think that you should or need to choose between the two views.
I think that both views are correct - but it is not the same thing they are looking at! That is probability to a Bayesian models the current uncertanty about an event whereas to a frequentist it models a frequency of correct guesses if the experiment could be repeated. Incidentially, the underlying probability theory (the events, probability measures and all that) applies to both schools. But although the terms (e.g. Probability, expectation, etc) used are interpreted in fundamentally different ways. Many times the two views can lead to the same thing. I pick the view which seems the most helpful in achieving my goal in a certain application.
A perhaps even more fundamental concern to have, is the view on probability theory itself. The "Are real things random or not?" questions. As a pragmatic engineer, actually, I do not care - what matters to me is that probabilistic models, are very good and convenient models for many phenomena. Applying statistics be it frequentist or Bayesian, lead to many good ways of guessing on phenomena which cannot be observed directly.
"That is probability to a Bayesian models the current uncertanty about an event whereas to a frequentist it models a frequency of correct guesses if the experiment could be repeated." -- This feels like a more faithful representation of what's going on, to me.
Thanks for the video! Nice way of explanation
0:56 "... heads up on my palm" ... ... which palm?
Yeah, I guess 100% based on the fact that there was a palm at the ready for each side.
And who should the palm belong to?
*on* my palm, not below my palm
@@kartikkalia01 "on" =\= "above"
@@6400ab wasn't it obvious what 'on' was used here for?
Sit on the chair.
Anyway, leave it. We are going into ambiguous linguistic terminology which is completely missing the point of this whole discussion.
How does this apply to quantum superposition?
what is the 'validity' of the question about probability of heads or tail once it is landed in your palm in this example is not clear ? what are its implications ?
Forgive my stupid question (which might be slightly off-topic), but doesn't it matter which side is facing up before the flip, how the coin is placed on the thumb, how much force it used for the flip, and some other factors (which may or may not be negligible)?
I don't know anything about statistics, but it sounds like when each group answers the "what probability is it that it's x?" question, they're focused on two different referents. The frequentists interpret the question as referring to the actual, determinate state of affairs in the world, while the Bayseians interpret it as an epistemological question, that is as a question about our knowledge. Two ways of interpreting what "probability" refers to.
I just stumbled across Florence Welch talking to me about statistics and I love this.
this is exactly why I struggled so hard to grasp statistics, despite having no problem with advanced probability theory - I think in a Bayesian way, but my course in statistics was frequentist.
1:00 I thought it was a trick question and you were going to show the coin stading up, stuck between your fingers, to make a point about how there might not be a probability. Guess that makes me a Bayesian.
If the coin is heads-up before tossing, it will always land heads-up, and vice-versa, IF it's landing on the palm of the person tossing the coin. If it's landing on hard surface, it can go anywhere due to the bounce / twist / turn of the coin multiple times before it comes to rest. So, which one am I?
Other than regularisation, I have yet to find a use for Bayes. The advantage of frequentist is it's really easy to see how it was abused
As a programmer, I kinda see both the same way. The Bayesian has a simplistic ideal model of the coin that they update. After 1000 tosses with 400 heads they may adjust their model to a 40% bias coin.
The frequentist is looking for a different model. The perfect one that is deterministic, and predicts each toss.
One is estimating the entropy of a sequence.
The other is looking for the lowest entropy model that generates the sequence.
The way I thought of it was that the chance that an event did/can/will happen is actually always either 100% or 0% and it is just a lack of knowledge that makes it appear otherwise. Or in other words, probability is like a measurement of our own ignorance (are we slightly unsure or very unsure? etc). I don't know if that shit's true, it just looks like it to me.
Well said! (That's how I see it too.)
Frequentism is realism about probabilities, Bayesianism is idealism about probabilities. Most scientists (still) are realists and this is why frequentism is the state of the art in statistical analysis and hypothesis testing. Recently various forms of anti-realism are being recognized not as a threat to science but as legitimate ways to address problems within science (e.g. constructive empiricism) and hence we'll see more Bayesian methods being applied. Machine learning is the most prominent field where this has already happened (and for good reasons - the things they're trying to build don't exist yet so there's nothing to discover about probabilities there, they have to be modeled).
Machine learning still relies on frequentist methods such as bootstrap aggregation.
What if I said both Bayesian and Frequentist response and can’t decide which one :(
I first answered 50%, then thought about it while she was peeking at the coin and said: 100%. Then thought about it a bit more and said: Meh, I have no idea. What does that make me?
Then you are an Bayesian.
Why?
A Frequenists would have answered "Frequenists" and then measure how often they were wrong.
You want to guess right and therefore say both (just like a Bayesian does with the coin)
What's the frequentist perspective on getting the model right? It always seemed to be like bayseans try to make that more explicit but I struggle to see a real distinction, but I'm kind of convinced (after adjusting my prior ;-) I just don't understand the semantic distinction that the frequentist perspective had with respect to (implicit) assumptions
Thank you for the simple explanation :) As far as I understand, the frequentist statistics is correct. However, from my point of view as a research scientist, the frequentist statistics is often irrelevant! Because I am often interested to know if my model or explanation of a complicated reality is consistent with the observations. These types of questions are consistently addressed within the framework of Bayesian statistics. On the other hand, the Bayesian approach is still missing an important ingredient. Bayesians still do not agree on how to construct priors! How does one construct a prior, which represents one's knowledge?
If you have no prior knowledge, this can be represented as a uniform distribution over all possibilities
In summary Bayesian are subjective and Frequentist are objective 🔥🔥
How is it possible that I only found this channel now? This stuff is brain-food-candy for any statistician like me! Keep it up :)
just came across this wonderful video, very simple explanation, read many articles but still confuse with the technical terminologies they have used in the paper. from this video within 5 minutes i have understood the concept. Thankyou Cassie for sharing wonderful knowledge with us. really appreciate it :)
If you have not yet seen the coin, according to your description, the frequentist would have to say 50%, because that's the probability they would guess correctly if they had to guess heads or tails. But that's the Bayesian approach. The Bayesian is in the subjective position to guess. The frequentist does not guess, he is concerned about the global asymptotic frequency. And the Bayesian does have a way to determine how well his assumptions were, the level of surprise. Given his assumptions, how likely or unlikely was the observation, how much did he need to change his prior beliefs.
In my undergraduate statistics courses, I essentially was indoctrinated to think in a frequentist way, to look for the result of a statistical experiment and say that I conclude with 95% confidence (or based on whatever your confidence level was) that a result was significant, or say that I have failed to reject the null hypothesis. So far, I still like that way of thinking.
Hm, I'm wondering whether I can say this?:
1) Frequentist statistic is an inductive approach - trying to infer properties of the population from collected data (which also includes evaluating the assumptions of properties of the population by analysing the likelihoods of data given these assumptions --> see significance testing).
2) Probability is deductive - "knowing" properties of the population and inferring properties (probabilities) of data points from that. (And Bayes specifically includes Beliefs, which can be updated).
P.S. I'm not sure how to handle the concepts probability and Bayes - are they the same or is Bayes a special case of probability or ...?
You're a damn good teacher madame! If you are not using that talent somewhere along your path, then it's a crying shame!
This video... is the best thing about COVID-19. I was hoping the world would start to get science more, but looking around, no, no. This video on the other hand, while it does not even mention Sars2, ticks the box. Proceed.
So, if I was to try and put that in terms I’ve spent some time with, I’d say:
A Bayesian attempt at ‘finding truth in uncertainty’/‘making predictions’ finds base rates relevant. So we cultivate relevance around the coin only landing on heads or tails, but do not place relevance on the physics of the coins’ trajectory and inertia, physical determinence, interaction with air molecules, etc etc. We use base rates as an end, and not a means to an end.
A Frequentist will cultivate relevance of those latter things, as they claim we shall assert we live in a determined universe, but in so far as we cannot fully gasp all the elements of that determination, we can use statistical models instead and judge their efficacy from the outcomes.
Is that right?
Loved this!
The chance of a coin landing heads/tails is always 50%. The current state of a coin is determined, which is a different question, despite it being hidden, there is a definitive state. The definitive state is that it is 100% side A or 0% side A, p(side A) = 50% still.
It's curious to think about probability and statistics theories in physics. In my perspective, the experimental physicists generally goes with a Frequentist mind, since the common mindset is to try the same experiment over and over and look what percentage they got a "good answer". In the other hand , the theorists care too much about perspective and information, actually the quantum theory is bounded to theses concepts, hence, the resolutions of the problems are made from a Bayesian mind. Your videos are awesome! Loved it!
I said 40 percent based upon the fact she had a hand that caught the coin at a non level planar and that the coin may be weighted slightly more on one side due to grime build up
please explain:
so, from a bayesian perspective, yes the coin has already landed, but the core of the question is what was the probability of it having landed on heads or tails? it can only ever be one of two twings, yes or no, blue or red, up or down, always 50% to be or not to be.
I love how you explained the 2 perspectives.
As a kid, I used to wonder what the space between the stove and the pot was called. As an adult, I had the same issue with frequentism, I just didn't know how to formulate the question.
So what to use in a/b testing?
actually at the end of Bayesian statistics it goes back to Frequentist style for example Gibbs Sampling, posterior predictive check
it needs a lost of sample which come from its own distribution that s why it calls generative in machine learning
There is no such thing as rigid distinction between the two, I use both, just not for the same reasons obviously. Why would you choose only one anyway? There isn't a better one, so don't choose, both are important, and both can be very useful to consider in a same situation to see different things, it helps resolve problems in (unusual sometimes but) effective ways.
I'm just gonna leave it here but if rings any bell to somebody: I try to never be content with my deductions or ways of seeing and conceiving things, so I try to force myself to see from perspectives where I'm always wrong, even if it's from stupid reasoning/perspectives, it helps see unexpected things and patterns sometimes where we expect them the least and it drastically help understanding notions of relativity.
So would you say frequentists go with the flow?
Cassie, very interesting, which one is best for online A/B testing in your personal opinion?
Interesting. I think what I am seeing here is that Frequentists must turn into Bayesians if they wish to use statistical methods to determine the likelihood of a system being in a specific state in the future relative to another possible state. For example, the probability of precipitation, simply because the Frequentists have to wait for the forecast valid time to arrive in order to have any chance (pardon the pun) to make their assessment.
Cassie, thank you for detailed explanation. Please, please, please tell us more about pros and cons of Bayesian vs Frequentist approaches in the business context.
What a beautiful philosophical view statistic perspective. Loved it!
I am binge watching your videos. Wish I’ve known you and your work before.
Statistical probability is a measure of ignorance, not certainty. Everything that Does happen always had a 100% chance of happening, we just didn't have enough information to know it. The two perspectives are perfectly compatible.
Also, knowledge is justified belief.
Agree on the first bit, but not on the second. Knowledge is not simply justified belief, some does occur that way but much is also direct knowledge that does not require a belief.
And what are the odds that both the Bayesian and Frequentist throughput are calculated simultaneously by a given individual?
What are the applications in real world ? Areas where they help
So, is there a problem in statistical analysis where a Bayesian and a Frequentist would come up with different, empirically distinguishable answers? And if so, which answer would turn out to be correct?
It's important to note that frequentist theory is an incomplete theory. Bayesian inference is a theory that represents reality better -- with more accuracy. It addresses uncertainty, for any state of knowledge.
It's also important to note that frequentists try to estimate a parameter (point/range estimate) for something.
Bayesians try to evaluate degrees of plausibilities among hypotheses for a specific parameter.
These are two different approaches to the problem of trying to figure out what the parameter is. Therefore the interpretations of them are also different!
The problem with this test is that it has no implication. The person on the other side of the table forms opinion but does he act differently? With your coin-tossing example if there are one Baysian and one Frequentist on the other side of the table and they want to engage with you in a game of chance are they going to bet differently on a coin that you have already tossed?
A better example would be for you to toss a coin once and show the income to One Baysian and One Frequentis. The outcome is Head. Then you ask them to bet on the next income to be Head. What odds the Baysian and Frequentis would agree to?
If I thought it couldn't be 50% on this instance because of the unequal forces applied to the coin. What does that make me?
Observational data. It is always full of known and unknown biases and confounding effects. Different people will have different opinions as to the sources and magnitudes of these effects. It is unreasonable to use frequentist statistics in these cases.
Where there is a formal experimental process (e.g. randomised controlled trials) then frequentist approaches are the way to go. The overall process is focussed around finding the truth (as far as possible).
The problem arises in applying frequentist approaches to observational data and then saying 'this is the truth'.
There is a lot more observational data then that from formal experiments, leading to a temptation to apply frequentist statistics where they are inappropriate.
Where there is only observational data we have many different opinions and in a scientific age that feels unsatisfactory - but that is just the way things are.
Is there a way to empirically prove there is a physical universe beyond perception?
Thank you for your clear explanation!
I think both perspectives can be beneficial in different scenarios, depending on what you’re trying to accomplish.
Watched this a few more times. As far as this example therein, the frequentist is orientated around what the truth of the outcome has been probabilistically. Initially past tense thinking, maybe past will become prologue, maybe it can't or won't. And the Bayesian may not care so much about whether the outcome should or should not be classified probabilistically in any technical sense, as the value of such a pursuit thereof is taken for granted by sheer fact of the problem being analyzed, short of any shenanigans, or accompanying thought experiments, as a natural extension of the input state, considerations toward and about the conditions and processes involved with how the outcome may likely come to fruition, or in a word or three, the driving phenomena methods pertaining to the event under consideration, and what's to follow upon the onset of the coin being flipped, etc,...blam outcome, assessment anew, etc. -- Whereas, frequentism lends itself to be willing to trade knowing the why of coin flipping, for any value that may come with being able to _efficiently_ analyze flipped coin outcomes' probability calculation(s) thereto.
This, absolutely have no idea why it's in recommendation.
Don't know why I watched the whole thing too.
The algorithm moves in mysterious ways, brother.
because google wants you to further separate yourself from others by now thinking about this
In part, it's an ASMR. Especially if your head is inbetween good pair of headsets.
@@JWhitty Jokes aside, this sounds terribly on point, looking at the current state of affairs.
@@dgodiex of course it's on point. 90% of what is put out by any entity with massive reach is to manipulate opinions. what the fuck is the point of pushing a psychology video to BILLIONS whose only real message is YOURE ALL DIFFERENT AND NOW GO THINK ABOUT IT? She keeps hinting at "what is right? what's more logical? EHHH..." and she leaves it open for people to start mentally pointing fingers. she's egging you on, begging you to judge them. its such bullshit and MATTERS 0%.
If it's philosophical, I'm surprised that the simple premise that 'Switching out of the default answer' as a question is by itself deviating out of the default... i.e. if I brush my teeth everyday the past week as it is my defaulted decision at the start of the week, but next week, everytime I brush, if I choose to contemplate if or not to brush before I do it... it's already not default... Hence Bayesian and Frequentist is simply what I would call a difference between '0 and 1' and '-1 and 1' when taking decisions... it doesn't matter how you encode your decisions... you could choose not to do it.. or you could choose to not do it... doesn't make a literal difference, only makes a difference in framing of your decision in manners where you consider inaction as action
Who are you @cassie Frequentist or Bayesian
I believe I cannot love this video enough. I've watched it over and over and recommended it to many people. But then again this is just my belief which I'm willing to change in the future based on the data. I believe this makes me biased towards being a Bayesian, but someone correct me if I'm wrong. 😇
Clear explanation, thanks. Will it be possible to have a mathematical explanation as well, such as doing the same analysis (for instance comparing mean across two groups) using Frequentist (a t-test) versus Bayesian approach (?) ?
Beautifully put. Very intuitive.