probability is the quantity most people are familiar with which deals with predicting new data given a known model ("what is the probability of getting heads six times in a row flipping this 50:50 coin?") while likelihood deals with fitting models given some known data ("what is the likelihood that this coin is/isn't rigged given that I just flipped heads six times in a row?"). I wanted to add this perspective because using the example in this clip, a likelihood quantity such as 0.12 is not meaningful to the layman unless it is explained exactly what 0.12 means: a measure of the sample's support for the assumed model i.e. low values either mean rare data or incorrect model!
That's what I was thinking. I've taught plenty of Probability courses, and I really wasn't sure what this "Likelihood" was supposed to be conceptually. The issue being that Likelihood as described here isn't really concept, it's just a computational tool used in the intermediate steps for fitting models. In fact, if you go a step further you turn the set of possible models into a probability space itself, and then Likelihood is itself a probability again.
Thank you for easy explanation!!! In addition.. The Probability of an event is 0... that is, 1/infinite. Therefore, We should compare the cumulative probability between events. But we can compare the y values between events. Definition of Likelihood in easy : y value of PDF. Countable Events : Likelihood = Probability. Continuous Events : Likelihood =/= Probability. Likelihood = PDF. Have a nice day!.
@@jamescollier3 when you say "10 percent" you are talking about probability (area under the curve). likelihood is instead just an instantaneous point on the curve. 0.12 does not equal "12 percent". it is at the moment just a number for one data point. you would compare it to another datapoint which would have its own likelihood given the assumed model, e.g. the likelihood of getting a 34g mouse is 0.15, or, it is more likely given the model that a randomly selected mouse is 34g instead of 32g. if you wanted to to quantify it in layman terms you would use probability instead. such as, given this model, 68% of the time the mouse should be 34g +/- 2.5g
Hi Josh, I really love how you simplify statistics concepts. After watching above video, I have this question, Does likelihood always have to be a single point and not a range? Can there be a question like, What is the likelihood of weighing a mouse between 32 and 34 grams? Will the likelihood also be a range in that case? Like between 0.12 and 0.13 or something like that?
That's a good question. The problem is that in normal conversation, "likelihood" and "probability" are interchangeable. So, in normal conversation, it makes sense to say "the likelihood of weighing something between 23 and 35 grams is X". So that's OK. However, the mathematical definition restricts it to a single point. So when we are deriving things we have to use the strict, mathematical definition. p.s. Thank you so much for supporting StatQuest!!! BAM!
Great work done till this point. Videos are great and reflect meticulous effort. However it seems we are multiplying oranges and apples in the hope of getting strawberries. I have searched lot of famous books but never seen anyone plugging in numbers into f(x) equation of normal or exponential or any continuous function in the hope of getting single discrete value. Infact we always take integral and put in limits to get probability of a range of values. Of x and that is F(x).
Right, so: - Probability is for predicting an outcome within a known system (eg. rolling fair dice) - Likelihood is for analysing an outcome when the system is not known for certain (eg. determining if particular dice actually are fair, or determining what curve is the best model for a dataset) I just learned a thing - thank you. :-)
I am a postdoc in neuroscience/psychiatry on a mission to brush up my stats knowledge. I can only repeat what others have already said: It's amazing how you break down and explain complicated topics in an understandable way. Thx so much for these videos.
When I was doing my neuroscience undergrad, I had to help the TAs in the Stats lab courses as I was the only person that understood math lol. Even still, I wish these videos existed when I was taking the course.
This is good stuff. Although I have taken 3 graduate level statistics courses, I struggle to explain the rationale behind the concepts. Which means, of course, that I lack deep learning of statistics. Your straightforward and graphic explanations are marvelous; even better than my stats professors. Thanks and I’m a subscriber now.
I never thought I would be saying I like stats. As you grow older, you will see the importance of stats in the real world you start to appreciate it more
Bam! I think what you say is true. The older I get, the more I appreciate the variation that I see in the world around me. And the more I appreciate variation, the more I appreciate statistics as a way to understand it.
I just noticed something interesting. In my native language (spanish) the word Likelihood doesn't have a special word to be defined, like Josh is saying in english where exists a difference between likelihood and probability, if one checks the translation of likelihood to spanish it would equal to "probability" so it appears on spanish the word just does not need to be differentiate but in english it is !
This problem is actually the same in English. In normal conversation, "probability" and "likelihood" are equal and mean the same thing. Only in statistics do they mean different things. This is why these terms are so easily confused, even by native english speakers.
In spanish, some professors use the word "hope" in addition to "probability." Years later, I find this video and suspect a lot happened that I didn't notice. 🤨
Oh man. I had thought you did these songs at the start just for the memes. But I checked out one or two songs from your discography. They're prettty good!
I am a little bit confused concerning the second examle because this is probability density function, not cumulative distribution function. Probability density function has probability density (not probability itself) on vertical axis. So why did you conclude that likelihood is 0,12? In my opinion, this is probability density. In order to see likelihood we have to swich to cumulative distribution function and look what Y-value correspondes to 34 grams.
The reason why we use a probability density function (PDF) is that a very large number, like 1,000,000 grams should have a very low likelihood - and the PDF ensures that is the case. If we used a cumulative density function (CDF) then the likelihood would be very large for a crazy large number, and that doesn't make sense.
That did actually also confuse me quite a bit at first as I thought the same, why is he describing the pdf. However, the thing is that normally you consider not just one sample but numerous, which form a product and that is also where it becomes clear what the likelihood is. I would suggest to maybe use multiple data points in the explanation since that is also how you are going to encounter it in most text books.
@@quAdxify That's a good idea, and that's what I have in all of the videos that show "likelihood in action", for the exponential, binomial and normal distribution: ruclips.net/video/p3T-_LMrvBc/видео.html ruclips.net/video/4KKV9yZCoM4/видео.html ruclips.net/video/Dn6b9fCIUpM/видео.html
Note that likelihood=0.12 doesn't mean that, given the observed data, those parameters have 12% of being the true parameters. The likelihood, in this case, just has a relative meaning. The degree to which data supports one parameter value versus another is measured by their likelihood ratio. To prove why PDF can be used as the "likelihood" and why maximizing likelihood is a good strategy for estimating distribution parameters is a different story (e.g., we must prove that maximizing the "likelihood" is equivalent to maximizing the PDF, and the parameter estimated by maximizing likelihood converges to the true parameters exponentially when the number of observed data point increases) In different foundations of statistics, the likelihood can mean different things. In Bayes inference, the likelihood has an absolute probability meaning, which says that "Given the parameter is true, what is the probability that I can observe this data".
So the probability of something being exactly 34g would be 0, but the likelihood of it being 34g is an actual number, if I’m understanding that right. So the confusion over likelihood being 0 is a confusion of probability vs likelihood, I guess.
this is the most understandable explanation out of all videos i've seen so far about the differences between probability and likelihood.. thankyou so much
Why not consider "Probability density" vs Likelihood, instead of talking about "Probability"? To me, probability densities are more directly related to likelihoods, than actual probabilities. For probability density we can use the pdf/pmf p(x|theta), where x is a variable and theta is fixed. The corresponding likelihood is a function that looks the exactly the same as the pdf/pmf except that x is fixed and theta is a variable: L(theta|x).
Thanks for this video. I'm a little confused about what you have mentioned about probability. You mentioned that probability is the area under the curve of distribution for a given interval. However if data is only a single point, the area is zero and it would contradict with this equation L(parameters; data) = P(data; parameters)
I must confess that I had a hard time understanding it too. (not knowing English is part of it, I've been playing the second video of the logistic regression series for more than 10 times) I think probability is when you evaluate the integral of the function in a certain range. And likelihood is when you evaluate the function at that point.
Still don't know what likelihood is. "The likelihood of weighing a 34 g mouse is this point on the curve and that is 0.12" AND "likelihoods are the y-axis values for fixed data points with distribution that can be moved". From these two core statements in the video, I still cannot use 'likelihood' in a sentence spoken to my father.
Couldn't help but type in Comment #300 I would have LOVED to be a Mathematician or a Statistician. But had to give up on that when I realized that I didn't have quite the "Talent Level" that my peers who were going in that direction had. Paul Erdos I'm not. A friend told me (please understand that this was in the mid 70s), "You're going to need AT LEAST a Masters Degree before you can go out and beg for a job. And in all likelihood, not only will you will need to write a Thesis to get that Degree, but you're going to have to pick a topic VERY Soon after you start your Masters Studies AT THE LATEST or you will be light-years behind your classmates. Most of them will have chosen their Thesis Topic during their Undergraduate days." The only topic I can recall having had Any interest in at that time was the Navier-Stokes Equations. But, I have seen where so-called "Authorities" argue about whether this is a physics or a math Equation. So much for that. Also, tried to read background material on the Hodge Conjecture and it might as well have been written in Sanskrit. Also, I was told, "If you can't get a job as a Mathematician or a Statistician, you can always be a teacher." Yeah right... I can honestly say that I never had even ONE teacher that "inspired" me in any Method, Manner or Fashion. And the number of teachers I would have loved to hire the Columbine Boys to "take care of" is Easily in two digits. So I sure as heck wasn't going to become one of them. Lastly, given my Life-long Hatred of school in general (me and Evariste Galois, among others), I saw that going into Accounting was a viable alternative, in that I was able to get a job with just the (then) four-year Bachelors Degree. The day I put all school in the rear-view mirror for Life, I remember saying, "This is how prisoners who just got paroled must feel." All that aside, to this day Math and Statistics remain two of my favorite hobbies. Since I was Lucky and Blessed enough to have been able to retire five years ago at age 55, I have all day, every day, to do what I LIKE to do, rather than what I HAD to do to survive. GREAT Video! Thank you, Sir! All Best!
@@ReTr093 That's good to know and I am happy for each and every one of them. But I am curious. Do you know if the typical requirement for getting job as a statistician is a Masters Degree? Or can they become employed with a Bachelors Degree? Thank you for your response. All Best!
Hello! I'm grinding for my categorical data analysis exam (what doesnt set me in the best mood) and have to say that the song at the beginning made me feel slightly better
The best way to understand likelihood is to see it in action. Check out how likelihood is used to find the optimal exponential distribution given some data: ruclips.net/video/p3T-_LMrvBc/видео.html
It's best understood through conditional probability. The symbol P(x|y) means the "probability density of x conditioned on y", and it is at the same time the "likelihood of y".
The way of you speaking is very similar to Baldi in Baldi's Basics in Education and Learning. Which makes me terrified some times, but i'm generally more terrified how rapid i learn watching your videos. Thank you.
So does it mean that the y-axis of the PDF is the likelihood of the distribution given the data points observed? If so, that would solve the problem that has been confusing me for so long!
Right! It seems he talks about the probability that the mouse has a weight between 33,5 and 34,499999 g. And then we talk again about an area under the graph as before. So the whole video is a fail.
Yes but he's not talking about the probability of the mouse weighing exactly 34g. The mouse weighs 34g. It's a given. A data point. The question is how likely this is given a distribution. That's what the likelihood is for.
You are absolutely correct, but please refer to the title of the video. *the likelihood of the **_distribution_** (with the stated parameters) given you had a mouse of 34g*
The likelihood of a specific data point (measurement) is the value of the pdf at that specific data point. (Values on the x axis and pdf/likelihood on the y axis) The probability for any specific exact measurement point, is 0 but probability of a range is the area under the pdf in that range The probability is of data given a distribution where as likelihood is the likelihood of a distribution given data.
@Mostafa I agree with what you 've written. Would you mind rephrasing that for discrete distributions? I get confused with the terms when differentiating between discrete and continuous distributions. :-/
I do see your point, but to me likelhood is just a probability mass or probability density, that's a function of the unknown parameters of the distribution, given a sample from that distribution.
Good video as usual. But I am abit confused. Please how did you arrive at 0.29 for the probability? I am sorry, I don't understand that calculation. Please could you briefly explain.
We calculate the area under the curve. You can do this by hand using calculus, or you can get a MS Excel (or some other computer program) to do it for you. I used a statistical language called R.
I was completely confused on the concepts, after referring lots of videos and confusing intuition I just came to this channel. The song you play at the starting of this video just refreshes the learning journey. The content you give with clear intuition makes me really very very very very very happy...
I've been scrolling through the comments looking for this confirmation! Thanks! Maybe Josh can add one of those "pop ups" to the video pointing out this minor error?
God ! So hard have I been through, to finally find a intelligent guy to know probability.Hi Josh Starmer Can I talk to you in private? Can I make friends with you.
This going to sound counter intuitive, but the probability of a mouse weighing exactly 34g is 0. That's because the probability is the integral, the area under the curve, from one point to another. If the width of that area is 0, then the area itself is 0. So, when ever you calculate probabilities, you do it for two different values. So 33.9999 to 34 would work, and you would get a positive value for the probability between 0 and 1. But the area under the curve from 34 to 34 is 0.
StatQuest makes me feel so happy... so very very very very very very very very..... Happy! StatQuest! I mean seriously, yeah!!!!!! love this channel from China!
Strange, almost every book I've read so far talk of P(data|distribution) as likelihood, and P(distribution|data) as posterior. Am I missing something here? 🤔
That is very interesting. The second part, P(distribution | data), is in fact a posterior, as you suspect. The "P" is the important part. It tells you to integrate the function. If it were "L", then we would a likelihood, and that would tell you evaluate the function a specific point. The first part, however, P( data | distribution) being called a likelihood is confusing. Even Bayesian folks tend to observe the "P" means "probability" and "L" means "likelihood" convention. That said, in Baysian statistics, you'll see likelihood functions written like this L( data | distribution). However, in this case, they are calculated just like L( distribution | data). The difference being that Bayesians let the parameters be random variables, and non-Bayesians only let the data be random variables.
P(distribution|data) = [P(data|distribution) * P(distribution)] / P(data) or in Bayesian Terms posterior = likelihood * prior. In the likelihood function we are given a fixed data set (the measurement) and we are postulating the distribution that data set came from. This is what Josh says in the video. Also, P(data) is a constant to make the posterior integrate to 1.
It's true - a discrete distribution would be a little easier to understand, but most people do t-tests, which are continuous, so I figured I'd start there. however, I may do another video that shows the discrete version.
This may be a silly R stat question but I thought the likelihood is calculated using the density function, dnorm, and if I run that code...dnorm(34,mean=34, sd=2.5) I get 0.159, which isn’t .21 Does any one know if I’m using the wrong function? or maybe using it incorrectly?
So just to close the loop, it looks like this is just an error in the video. I believe I’m right about the likelihood calculation using a single observation of 34 grams with those parameters...it isn’t .21 and you can confirm this in R with the dnorm function. Making instructional videos is time consuming and takes many reviews for edits. My hunch it was just a typo.
Than how do you find the probability of a mouse to have exactly 32 grams ? The area under a single point is 0. But I am not sure that the probability is also 0...
The probability is 0. Here's a way to think about it - when we weight a mouse that is exactly 32 grams, then the weight = 32.00000000000.... The more accurate our measurement is, the lower the probability that we will measure something that is exactly a specific value.
@@statquest Now I remembered the explanation of my teacher ... If you through a dice with 6 faces, probability of 1 face to show up is 1/6 . If you throw a dice of 32 faces, the probability of 1 face to show up is 1 /32. If you throw a dice with an infinity number of faces (a sphere) the probability to land on a face is 1 / infinity = 0 ....
Bumped into this video, and glad I did! Please make a video using a discrete distribution. That'll really help differentiate between likelihood and probability. The problem with Y values being in a continuous domain is that, by definition, we'll always have to just say that the P(mouse weight = 32) = 0, and there ends any scope for comparing it to L(32) :-)
ok, so the difference between probability an likelihood is the difference between an inegral and the value of the distribution-function... which means, the 34g mouse has a likelihood of 12% but a probability of 0%, since the interval of integration is 0? i understand cpu's, but not statistics...
Not exactly. Probability is the integral from a to b of f(x)dx, likelihood is just f(x). If you remember calculus, any integral from a to a is zero, even if the interior function is not.
@@ronaldjensen2948 I've randomly stumbled on the same video again and yes, it says that likelihood is the PDF. I don't know how me from ten months ago arrived at his conclusion.
@@statquest Btw, I just stumbled on this channel and it's so helpful, thank you so much. By far the best explanations I've seen. Hats off to you. And you even laugh at dad jokes! :)
Thanks Joshua! ...umm... at TIME 1:25 how did you calculate the area under the curve to be 0.29. Also, shouldn't there be units (of distance) to this figure? The weight-in-grams on the abscissa psychologically blocks me to think of the area in units of distance. Please help!
I have the same question. If σ = 2.5 and you march out 2.5 increments from the μ of 32, the area under the curve would be 34%. I'm wondering how by marching out 2 increments from μ, the area above this distance equals 29% of the curve, rather than 27%. I've scoured the other replies and don't see anyone else disputing the point so I figure my understanding is flawed. Could someone please show me how he arrived at 29%?
@@jedwatling I am also confused by this. Like you, I think that the probability of a mouse weighing between 32 and 34 would appear to be 0.272. This is because the standard deviation is 2.5 (meaning 34.5 is the 68th percentile), and thus 2 would be 34. 2 divided by 2.5 is 0.8, and 0.8 multiplied by 34 is 27.2. I'm not sure how 0.29 was arrived at instead. I wonder where we're going wrong?
i thought that the probability of a certain value in continous distribution is always 0. you dont have discrete weights like 32, 33 etc, but 32.00000001 etc. the probability of a mouse being exactly 32 is zero.
That is exactly right. However, the likelihood for a single point is not zero. The reason for this might be more obvious if you saw likelihoods in action. Here's a video that shows how likelihoods are used to estimate parameters for the exponential distribution: ruclips.net/video/p3T-_LMrvBc/видео.html
@@georgesmith3022 No, it's zero. For example, the area of a rectangle that has 0 width is 0. So the area under the curve of a continuous statistical distribution, like the normal distribution, with 0 width is 0.
Nice explanation but i m afraid i still dont understand whats likelihood..can somebody pls explain in plain words..josh has explained in terms of formula
say you measure one mouse. ONLY one mouse. You get 34g. You know nothing about mice? according to your single experiment it is probably best to put the mean of mice around 34g because that gives the max likelihood for your experiment (i.e because the mean has highest probabilityy. For all you know now the mean is 34g and thats it but you only did 1 now you go ahead and do 2 mass weights one at 34g and one happened to be at 30g. According to your original distribution where mean was at 34 this would not give maximum likelyhood because the mass at 30g is very little represented. You will have to shift your distributiion to MAXIMIZE likelihood. To maximize the probability of all measurements
@@statquest Thank you for your reply. Sorry I should phrase my question more clearly -- looking at your video, the likelihood seems to be the probability density value of the distribution, except that what changes in the likelihood function p(X|theta) is "theta" instead of "X" as in the probability density function -- so in other words, the value of the likelihood function p(x_1 | theta_1) is equal to the probability density value p(x_1 | theta_1) from the probability density function, but the likelihood function is not the probability density function since the variables (whose values change) of these two functions are different
Thank you for this! Both probability and likelihood translate to "Wahrscheinlichkeit" in German so I'm having quite a hard time wrapping my head around this. Also strangely all my stochastic education has been kinda vague on everything even at uni... This helped though!
probability is the quantity most people are familiar with which deals with predicting new data given a known model ("what is the probability of getting heads six times in a row flipping this 50:50 coin?") while likelihood deals with fitting models given some known data ("what is the likelihood that this coin is/isn't rigged given that I just flipped heads six times in a row?"). I wanted to add this perspective because using the example in this clip, a likelihood quantity such as 0.12 is not meaningful to the layman unless it is explained exactly what 0.12 means: a measure of the sample's support for the assumed model i.e. low values either mean rare data or incorrect model!
That's exactly right! Thanks for posting your comment.
Thanks for clarification
That's what I was thinking. I've taught plenty of Probability courses, and I really wasn't sure what this "Likelihood" was supposed to be conceptually.
The issue being that Likelihood as described here isn't really concept, it's just a computational tool used in the intermediate steps for fitting models.
In fact, if you go a step further you turn the set of possible models into a probability space itself, and then Likelihood is itself a probability again.
Thank you for easy explanation!!!
In addition..
The Probability of an event is 0... that is, 1/infinite. Therefore, We should compare the cumulative probability between events. But we can compare the y values between events.
Definition of Likelihood in easy : y value of PDF.
Countable Events : Likelihood = Probability.
Continuous Events : Likelihood =/= Probability. Likelihood = PDF.
Have a nice day!.
@@jamescollier3 when you say "10 percent" you are talking about probability (area under the curve). likelihood is instead just an instantaneous point on the curve. 0.12 does not equal "12 percent". it is at the moment just a number for one data point. you would compare it to another datapoint which would have its own likelihood given the assumed model, e.g. the likelihood of getting a 34g mouse is 0.15, or, it is more likely given the model that a randomly selected mouse is 34g instead of 32g. if you wanted to to quantify it in layman terms you would use probability instead. such as, given this model, 68% of the time the mouse should be 34g +/- 2.5g
Hi Josh, I really love how you simplify statistics concepts. After watching above video, I have this question, Does likelihood always have to be a single point and not a range? Can there be a question like, What is the likelihood of weighing a mouse between 32 and 34 grams? Will the likelihood also be a range in that case? Like between 0.12 and 0.13 or something like that?
That's a good question. The problem is that in normal conversation, "likelihood" and "probability" are interchangeable. So, in normal conversation, it makes sense to say "the likelihood of weighing something between 23 and 35 grams is X". So that's OK. However, the mathematical definition restricts it to a single point. So when we are deriving things we have to use the strict, mathematical definition.
p.s. Thank you so much for supporting StatQuest!!! BAM!
Great work done till this point. Videos are great and reflect meticulous effort. However it seems we are multiplying oranges and apples in the hope of getting strawberries. I have searched lot of famous books but never seen anyone plugging in numbers into f(x) equation of normal or exponential or any continuous function in the hope of getting single discrete value.
Infact we always take integral and put in limits to get probability of a range of values. Of x and that is F(x).
@@statquest single point is discrete
Thanks!
Wow! Thank you very much for supporting StatQuest! BAM! :)
The likelihood of a point on a continuous line is epsilon of zero.
Right, so:
- Probability is for predicting an outcome within a known system (eg. rolling fair dice)
- Likelihood is for analysing an outcome when the system is not known for certain (eg. determining if particular dice actually are fair, or determining what curve is the best model for a dataset)
I just learned a thing - thank you. :-)
yep.
Thanks!
Wow!!! Thank you so much for your support! BAM! :)
I am a postdoc in neuroscience/psychiatry on a mission to brush up my stats knowledge. I can only repeat what others have already said: It's amazing how you break down and explain complicated topics in an understandable way. Thx so much for these videos.
Thanks!
When I was doing my neuroscience undergrad, I had to help the TAs in the Stats lab courses as I was the only person that understood math lol. Even still, I wish these videos existed when I was taking the course.
Seriously, please don't stop making these! You really nail the topics in the most perfect time, and always explain them in awesome ways :)
Your intro songs have really grown on me. You are like the Bob Ross of Statistics.
Very well put
Haha agreed!
Now I’m worried that if I subscribe I’m going to loose my taste in music.
Totally agree Bob Ross of Statistics haha
Bob Ross was a painter, not a musician...
This is good stuff. Although I have taken 3 graduate level statistics courses, I struggle to explain the rationale behind the concepts. Which means, of course, that I lack deep learning of statistics. Your straightforward and graphic explanations are marvelous; even better than my stats professors. Thanks and I’m a subscriber now.
Thank you very much! :)
statquest makes feel very very very happy indeed!
Hooray!!! :)
I never thought I would be saying I like stats. As you grow older, you will see the importance of stats in the real world you start to appreciate it more
Bam! I think what you say is true. The older I get, the more I appreciate the variation that I see in the world around me. And the more I appreciate variation, the more I appreciate statistics as a way to understand it.
So, Can we say that likelihood is something like training a model and probability like predicting by using that model . Correct me if I'm wrong 💢
That's not unreasonable. Likelihood are generally use for training and probabilities are used once we have fit the model.
wow!! that was the most clearly explained math video i have ever seen, thank you so much
Thank you! :)
When he says "BAM", that's when I remember to press "Like"
BAM! :)
I just noticed something interesting. In my native language (spanish) the word Likelihood doesn't have a special word to be defined, like Josh is saying in english where exists a difference between likelihood and probability, if one checks the translation of likelihood to spanish it would equal to "probability" so it appears on spanish the word just does not need to be differentiate but in english it is !
This problem is actually the same in English. In normal conversation, "probability" and "likelihood" are equal and mean the same thing. Only in statistics do they mean different things. This is why these terms are so easily confused, even by native english speakers.
In spanish, some professors use the word "hope" in addition to "probability." Years later, I find this video and suspect a lot happened that I didn't notice. 🤨
@@diegofabianledesmamotta5139 In polish we used to call expected value "mathematical hope". We don't differentiate probability and likelihood too.
"Jibber Jabber clearly explained" is t-shirt worthy!!!
That's a great idea! BAM! :)
Oh man. I had thought you did these songs at the start just for the memes. But I checked out one or two songs from your discography. They're prettty good!
Thanks! :)
This feels weird for me, In spanish there isnt a word for likelihood.
Interesting!
Creo que podria ser posibilidad vs probabilidad
I am a little bit confused concerning the second examle because this is probability density function, not cumulative distribution function. Probability density function has probability density (not probability itself) on vertical axis. So why did you conclude that likelihood is 0,12? In my opinion, this is probability density. In order to see likelihood we have to swich to cumulative distribution function and look what Y-value correspondes to 34 grams.
The reason why we use a probability density function (PDF) is that a very large number, like 1,000,000 grams should have a very low likelihood - and the PDF ensures that is the case. If we used a cumulative density function (CDF) then the likelihood would be very large for a crazy large number, and that doesn't make sense.
In all likelihood you may not fully understand the difference between probability density functions and cumulative density functions :-/
That did actually also confuse me quite a bit at first as I thought the same, why is he describing the pdf. However, the thing is that normally you consider not just one sample but numerous, which form a product and that is also where it becomes clear what the likelihood is. I would suggest to maybe use multiple data points in the explanation since that is also how you are going to encounter it in most text books.
@@quAdxify That's a good idea, and that's what I have in all of the videos that show "likelihood in action", for the exponential, binomial and normal distribution:
ruclips.net/video/p3T-_LMrvBc/видео.html
ruclips.net/video/4KKV9yZCoM4/видео.html
ruclips.net/video/Dn6b9fCIUpM/видео.html
Note that likelihood=0.12 doesn't mean that, given the observed data, those parameters have 12% of being the true parameters. The likelihood, in this case, just has a relative meaning. The degree to which data supports one parameter value versus another is measured by their likelihood ratio.
To prove why PDF can be used as the "likelihood" and why maximizing likelihood is a good strategy for estimating distribution parameters is a different story (e.g., we must prove that maximizing the "likelihood" is equivalent to maximizing the PDF, and the parameter estimated by maximizing likelihood converges to the true parameters exponentially when the number of observed data point increases)
In different foundations of statistics, the likelihood can mean different things. In Bayes inference, the likelihood has an absolute probability meaning, which says that "Given the parameter is true, what is the probability that I can observe this data".
Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/
StatQuest , you're the best when it comes to "making it Simple"
Thank you! :)
So the probability of something being exactly 34g would be 0, but the likelihood of it being 34g is an actual number, if I’m understanding that right. So the confusion over likelihood being 0 is a confusion of probability vs likelihood, I guess.
What confusion over the likelihood being 0?
After spending 2 hours on RUclips learning about probability and anything related to it, I landed on this video and I want to say this: I LOVE YOU
BAM! :)
Statsquest makes me feel so happy
So very very very very very very very very very happy
:)
Duuuude, I've been doing data science for about 5 years now and stats for a lot longer and this is the best explanation every. I'm stealing this!
Hooray! :)
this is the most understandable explanation out of all videos i've seen so far about the differences between probability and likelihood.. thankyou so much
Glad it was helpful!
Thank you man, THANKS A LOT
seriously. Finally I got it, omg
Hooray!!! That's awesome! :)
Why not consider "Probability density" vs Likelihood, instead of talking about "Probability"? To me, probability densities are more directly related to likelihoods, than actual probabilities. For probability density we can use the pdf/pmf p(x|theta), where x is a variable and theta is fixed. The corresponding likelihood is a function that looks the exactly the same as the pdf/pmf except that x is fixed and theta is a variable: L(theta|x).
Thanks for this video. I'm a little confused about what you have mentioned about probability. You mentioned that probability is the area under the curve of distribution for a given interval. However if data is only a single point, the area is zero and it would contradict with this equation L(parameters; data) = P(data; parameters)
For continuous data, likelihoods do not equal probabilities. This is only the case for discrete data.
I must confess that I had a hard time understanding it too. (not knowing English is part of it, I've been playing the second video of the logistic regression series for more than 10 times) I think probability is when you evaluate the integral of the function in a certain range. And likelihood is when you evaluate the function at that point.
Still don't know what likelihood is. "The likelihood of weighing a 34 g mouse is this point on the curve and that is 0.12" AND "likelihoods are the y-axis values for fixed data points with distribution that can be moved". From these two core statements in the video, I still cannot use 'likelihood' in a sentence spoken to my father.
The best way to understand likelihoods are to see them in action. Here's a great example: ruclips.net/video/p3T-_LMrvBc/видео.html
Couldn't help but type in Comment #300
I would have LOVED to be a Mathematician or a Statistician. But had to give up on that when I realized that I didn't have quite the "Talent Level" that my peers who were going in that direction had. Paul Erdos I'm not.
A friend told me (please understand that this was in the mid 70s), "You're going to need AT LEAST a Masters Degree before you can go out and beg for a job. And in all likelihood, not only will you will need to write a Thesis to get that Degree, but you're going to have to pick a topic VERY Soon after you start your Masters Studies AT THE LATEST or you will be light-years behind your classmates. Most of them will have chosen their Thesis Topic during their Undergraduate days." The only topic I can recall having had Any interest in at that time was the Navier-Stokes Equations. But, I have seen where so-called "Authorities" argue about whether this is a physics or a math Equation. So much for that. Also, tried to read background material on the Hodge Conjecture and it might as well have been written in Sanskrit.
Also, I was told, "If you can't get a job as a Mathematician or a Statistician, you can always be a teacher." Yeah right... I can honestly say that I never had even ONE teacher that "inspired" me in any Method, Manner or Fashion. And the number of teachers I would have loved to hire the Columbine Boys to "take care of" is Easily in two digits. So I sure as heck wasn't going to become one of them.
Lastly, given my Life-long Hatred of school in general (me and Evariste Galois, among others), I saw that going into Accounting was a viable alternative, in that I was able to get a job with just the (then) four-year Bachelors Degree. The day I put all school in the rear-view mirror for Life, I remember saying, "This is how prisoners who just got paroled must feel."
All that aside, to this day Math and Statistics remain two of my favorite hobbies. Since I was Lucky and Blessed enough to have been able to retire five years ago at age 55, I have all day, every day, to do what I LIKE to do, rather than what I HAD to do to survive.
GREAT Video! Thank you, Sir! All Best!
Funny how things changed. Statisticians get hired straight out of school now,and no way in hell it's a teaching gig.
@@ReTr093 That's good to know and I am happy for each and every one of them. But I am curious. Do you know if the typical requirement for getting job as a statistician is a Masters Degree? Or can they become employed with a Bachelors Degree?
Thank you for your response. All Best!
Hello! I'm grinding for my categorical data analysis exam (what doesnt set me in the best mood) and have to say that the song at the beginning made me feel slightly better
bam! :)
Maybe this seems overly simple for some, but this was awesome! Thank you!
came here after watching his logistic regression vids..the clearity of these topics is insane!! thanks a lot :)
Glad it was helpful!
Yeah, the clarity of this guy's explanations are off da chartZz!!
The likelihood part confused me...what here is shown as likelihood sounds more like hypth testing
The best way to understand likelihood is to see it in action. Check out how likelihood is used to find the optimal exponential distribution given some data: ruclips.net/video/p3T-_LMrvBc/видео.html
It's best understood through conditional probability. The symbol P(x|y) means the "probability density of x conditioned on y", and it is at the same time the "likelihood of y".
The way of you speaking is very similar to Baldi in Baldi's Basics in Education and Learning. Which makes me terrified some times, but i'm generally more terrified how rapid i learn watching your videos. Thank you.
bam!
Crisp, concise and to the point! Instantly cleared my confusion!
Hooray! :)
So does it mean that the y-axis of the PDF is the likelihood of the distribution given the data points observed? If so, that would solve the problem that has been confusing me for so long!
Yes, that is correct. The likelihoods for a set of data are the y-axis coordinates.
Holy sh*t! My head blown twice! Double BAM!!!
Hooray! :)
Best explanation I have seen of probability and likelihood. Thank you so much..
Glad it was helpful!
The probability of a mouse weighing exactly 34g Is IS ZERO
Right! It seems he talks about the probability that the mouse has a weight between 33,5 and 34,499999 g. And then we talk again about an area under the graph as before. So the whole video is a fail.
Yeah you need to define conditional probabilities differently for that case.
Yes but he's not talking about the probability of the mouse weighing exactly 34g. The mouse weighs 34g. It's a given. A data point.
The question is how likely this is given a distribution. That's what the likelihood is for.
he never said probability, he said likelihood.
You are absolutely correct, but please refer to the title of the video. *the likelihood of the **_distribution_** (with the stated parameters) given you had a mouse of 34g*
The likelihood of a specific data point (measurement) is the value of the pdf at that specific data point. (Values on the x axis and pdf/likelihood on the y axis)
The probability for any specific exact measurement point, is 0 but probability of a range is the area under the pdf in that range
The probability is of data given a distribution where as likelihood is the likelihood of a distribution given data.
@Mostafa I agree with what you 've written. Would you mind rephrasing that for discrete distributions?
I get confused with the terms when differentiating between discrete and continuous distributions. :-/
as a student who majors in statistics, all of your videos are so helpful! thank you❤
Weird that I get recommended this when I'm in a statistical thermodynamics class (help they are in the walls)
Weird!
I do see your point, but to me likelhood is just a probability mass or probability density, that's a function of the unknown parameters of the distribution, given a sample from that distribution.
I got MBA in data science and I didn't know this.
How the fuck did I graduate.
:)
Yeah, but what's mouse's name? And why do you have a mouse fetish?
Jajaja he loves mouses but his stats videos are very nice.
Good video as usual. But I am abit confused. Please how did you arrive at 0.29 for the probability? I am sorry, I don't understand that calculation. Please could you briefly explain.
We calculate the area under the curve. You can do this by hand using calculus, or you can get a MS Excel (or some other computer program) to do it for you. I used a statistical language called R.
@@statquest OK sir! Thanks. Thank you so much, I am grateful
I was completely confused on the concepts, after referring lots of videos and confusing intuition I just came to this channel. The song you play at the starting of this video just refreshes the learning journey. The content you give with clear intuition makes me really very very very very very happy...
Awesome! :)
There is an error, I think.
L(mean=34 and std = 2.5 | mouse weighs 34 grams) = 0.16,
not 0.21 as they pointed out in the video, right?
You are correct! That's a typo. :(
I've been scrolling through the comments looking for this confirmation! Thanks! Maybe Josh can add one of those "pop ups" to the video pointing out this minor error?
God ! So hard have I been through, to finally find a intelligent guy to know probability.Hi Josh Starmer Can I talk to you in private? Can I make friends with you.
Can I talk to you in private? Can I make friends with you.
edenlove 828 hotmail.
What is the probability of mouse weighing exactly 34g in this example? Isn't it same as that of likelihood?? I am bit confused.. Please help..
This going to sound counter intuitive, but the probability of a mouse weighing exactly 34g is 0. That's because the probability is the integral, the area under the curve, from one point to another. If the width of that area is 0, then the area itself is 0. So, when ever you calculate probabilities, you do it for two different values. So 33.9999 to 34 would work, and you would get a positive value for the probability between 0 and 1. But the area under the curve from 34 to 34 is 0.
StatQuest with Josh Starmer thank you for the explanation.... Counter intuitive it is... Let me study..
BAM! Thank you Josh, you explain concepts with such clarity and ease!
StatQuest makes me feel happyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy!!!!!!🤩
:)
StatQuest makes me feel so happy... so very very very very very very very very..... Happy! StatQuest! I mean seriously, yeah!!!!!! love this channel from China!
Thank you very much! :)
Still, what's the physical significance of likelihood?
Gottfried Leibniz my question is how do monads fit into likelihood? 🤔
Strange, almost every book I've read so far talk of P(data|distribution) as likelihood, and P(distribution|data) as posterior. Am I missing something here? 🤔
That is very interesting. The second part, P(distribution | data), is in fact a posterior, as you suspect. The "P" is the important part. It tells you to integrate the function. If it were "L", then we would a likelihood, and that would tell you evaluate the function a specific point. The first part, however, P( data | distribution) being called a likelihood is confusing. Even Bayesian folks tend to observe the "P" means "probability" and "L" means "likelihood" convention. That said, in Baysian statistics, you'll see likelihood functions written like this L( data | distribution). However, in this case, they are calculated just like L( distribution | data). The difference being that Bayesians let the parameters be random variables, and non-Bayesians only let the data be random variables.
P(distribution|data) = [P(data|distribution) * P(distribution)] / P(data) or in Bayesian Terms posterior = likelihood * prior. In the likelihood function we are given a fixed data set (the measurement) and we are postulating the distribution that data set came from. This is what Josh says in the video. Also, P(data) is a constant to make the posterior integrate to 1.
Τhis is my first video here...interesting .greetings from Greece
Thanks for watching!
So probability is for a range while likelihood is for a point
yes!
great vid, but I almost feel that it would've been much more clear with discrete distribution.
It's true - a discrete distribution would be a little easier to understand, but most people do t-tests, which are continuous, so I figured I'd start there. however, I may do another video that shows the discrete version.
This may be a silly R stat question but I thought the likelihood is calculated using the density function, dnorm, and if I run that code...dnorm(34,mean=34, sd=2.5) I get 0.159, which isn’t .21
Does any one know if I’m using the wrong function? or maybe using it incorrectly?
Edward M suggested using pnorm, but I don’t think that is right either. Using that function you get the expected 0.5.
So just to close the loop, it looks like this is just an error in the video. I believe I’m right about the likelihood calculation using a single observation of 34 grams with those parameters...it isn’t .21 and you can confirm this in R with the dnorm function.
Making instructional videos is time consuming and takes many reviews for edits. My hunch it was just a typo.
Amazing videos, can you do a playlist on bayesian statistics?
Than how do you find the probability of a mouse to have exactly 32 grams ? The area under a single point is 0. But I am not sure that the probability is also 0...
The probability is 0. Here's a way to think about it - when we weight a mouse that is exactly 32 grams, then the weight = 32.00000000000.... The more accurate our measurement is, the lower the probability that we will measure something that is exactly a specific value.
@@statquest BAM !!!
@@statquest Now I remembered the explanation of my teacher ... If you through a dice with 6 faces, probability of 1 face to show up is 1/6 . If you throw a dice of 32 faces, the probability of 1 face to show up is 1 /32. If you throw a dice with an infinity number of faces (a sphere) the probability to land on a face is 1 / infinity = 0 ....
This was a very clean explanation of probability and likelihood.
Thanks!
Thank you! :)
This is the best explanation i've seen ever
Thanks!
This is the best explanation I've ever seen! and I like your intro song as well!
Hooray! :)
DOULBLE BAM
YES!
Bumped into this video, and glad I did!
Please make a video using a discrete distribution. That'll really help differentiate between likelihood and probability. The problem with Y values being in a continuous domain is that, by definition, we'll always have to just say that the P(mouse weight = 32) = 0, and there ends any scope for comparing it to L(32) :-)
I really appreciate for saving my life..
bam! :)
Thank you for solving my questions that keeps staying on my mind for years. This helps a lot!
I wish i'd known you sooner, keep up the good work!
Thanks!
You get an automatic like just for the intro! Thanks for the video.
Hooray!!!! You're welcome. :)
ok, so the difference between probability an likelihood is the difference between an inegral and the value of the distribution-function...
which means, the 34g mouse has a likelihood of 12% but a probability of 0%, since the interval of integration is 0?
i understand cpu's, but not statistics...
That still makes "likelihood" a probability though.
no
no
Not exactly. Probability is the integral from a to b of f(x)dx, likelihood is just f(x). If you remember calculus, any integral from a to a is zero, even if the interior function is not.
@@ronaldjensen2948
I've randomly stumbled on the same video again and yes, it says that likelihood is the PDF. I don't know how me from ten months ago arrived at his conclusion.
Wow, I simply had no idea mice lifted weights nevermind that you could statistically analyse them.
:)
@@statquest Btw, I just stumbled on this channel and it's so helpful, thank you so much. By far the best explanations I've seen. Hats off to you. And you even laugh at dad jokes! :)
@@davidmurphy563 bam!
Wish I had seen this before I made my Baysian classifier. Thanks a lot for a great video!
Paul Burger why should someone cresate a NB classifier if there are plenty of them?
What is the likelihood in a discrete distribution, or does this only apply to continuous ones?
For a discrete distribution, the likelihood and the probability are the same.
If you'd like to see likelihood in action with a discrete distribution, check out: ruclips.net/video/4KKV9yZCoM4/видео.html
So the likelihood is somewhat like the derivative of the probability?
no, it's just the value of the distribution at that point, not the slope of the distribution
It sure seems that the probability is the integral of the likelihood.
Thanks Joshua! ...umm... at TIME 1:25 how did you calculate the area under the curve to be 0.29. Also, shouldn't there be units (of distance) to this figure? The weight-in-grams on the abscissa psychologically blocks me to think of the area in units of distance. Please help!
"height of the curve is scaled" ... what does this exactly mean?
I have the same question. If σ = 2.5 and you march out 2.5 increments from the μ of 32, the area under the curve would be 34%. I'm wondering how by marching out 2 increments from μ, the area above this distance equals 29% of the curve, rather than 27%. I've scoured the other replies and don't see anyone else disputing the point so I figure my understanding is flawed. Could someone please show me how he arrived at 29%?
@@jedwatling I am also confused by this. Like you, I think that the probability of a mouse weighing between 32 and 34 would appear to be 0.272. This is because the standard deviation is 2.5 (meaning 34.5 is the 68th percentile), and thus 2 would be 34. 2 divided by 2.5 is 0.8, and 0.8 multiplied by 34 is 27.2. I'm not sure how 0.29 was arrived at instead. I wonder where we're going wrong?
i thought that the probability of a certain value in continous distribution is always 0. you dont have discrete weights like 32, 33 etc, but 32.00000001 etc. the probability of a mouse being exactly 32 is zero.
That is exactly right. However, the likelihood for a single point is not zero. The reason for this might be more obvious if you saw likelihoods in action. Here's a video that shows how likelihoods are used to estimate parameters for the exponential distribution: ruclips.net/video/p3T-_LMrvBc/видео.html
@@statquest ok I meant it tends towards 0. So even 0.1 is a big value. But i believe u know better math than me.
@@georgesmith3022 No, it's zero. For example, the area of a rectangle that has 0 width is 0. So the area under the curve of a continuous statistical distribution, like the normal distribution, with 0 width is 0.
Great video 👌🏼🙌🏽👍🏽!!
Thank you!
Thanks Joshua! I love your video series on probability and likelihood :)
Thanks for saving my computational statistics
BAM! :)
Yes! I'm finding this funny, fascinating and awesome! But I am very high.
40 grams! That’s one fat mouse 😁
:)
did Donald Trump write your lyrics? It was very very very good. Studying stats from Sydney. I come here because I don't understand uni my lectures :(
Hooray! I'm glad to hear that the video was helpful. :)
Actually makes things so much more intuitive, thank you!
Hooray! :)
You are the best and easiest in statistics
Thank you! :)
As you said ，so clearly explained，Thank you very much.
You are welcome!!! I'm glad you like the video. :)
Anybody else think he was talking about tiny weights that you put on a scale when he said mouse weights? Lmao
I love it! :)
so so so so great, THANK YOU SO SO SO SO MUCH
Thanks!
Nice explanation but i m afraid i still dont understand whats likelihood..can somebody pls explain in plain words..josh has explained in terms of formula
say you measure one mouse. ONLY one mouse. You get 34g. You know nothing about mice? according to your single experiment it is probably best to put the mean of mice around 34g because that gives the max likelihood for your experiment (i.e because the mean has highest probabilityy. For all you know now the mean is 34g and thats it but you only did 1
now you go ahead and do 2 mass weights one at 34g and one happened to be at 30g. According to your original distribution where mean was at 34 this would not give maximum likelyhood because the mass at 30g is very little represented. You will have to shift your distributiion to MAXIMIZE likelihood. To maximize the probability of all measurements
as usual amazing videos by StatQuest
Glad you like them!
Finally someone from the USA using metric measurements.
Like the songs on bandcamp man!
Thank you!
So is likelihood the probability density then>??!!
It's the y-axis coordinate.
@@statquest Thank you for your reply. Sorry I should phrase my question more clearly -- looking at your video, the likelihood seems to be the probability density value of the distribution, except that what changes in the likelihood function p(X|theta) is "theta" instead of "X" as in the probability density function -- so in other words, the value of the likelihood function p(x_1 | theta_1) is equal to the probability density value p(x_1 | theta_1) from the probability density function, but the likelihood function is not the probability density function since the variables (whose values change) of these two functions are different
Your intro is terrible I have to say it's obligated from my conscience
Stupid comment. Is not useful.
Thank you for this! Both probability and likelihood translate to "Wahrscheinlichkeit" in German so I'm having quite a hard time wrapping my head around this. Also strangely all my stochastic education has been kinda vague on everything even at uni...
This helped though!
bam!
Shyeah, right! Try telling this to the editors of the Wikipedia article on Probability.