A visual guide to Bayesian thinking
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- Опубликовано: 4 июл 2024
- I use pictures to illustrate the mechanics of "Bayes' rule," a mathematical theorem about how to update your beliefs as you encounter new evidence. Then I tell three stories from my life that show how I use Bayes' rule to improve my thinking.
before video : chances of me being a millionaire 0.1%
after video : i applied bayesian thinking (remembered my priors) , now the chance is 0.0001%
What was the new piece of information you used to update your priors? I'd love to see the full calculation. ;)
Reality bites!
asdfghyter fact that he is wasting his time on RUclips might be one of them :p
yeah in America there's 10M millioniares. That's 3.33% of the population. If you save your money not becoming a millionaire is impossible unless you are 50 yrsold, or have an IQ below ~90ish probably
Sudhamsu
You live to the ripe old age of 125 :)
If a repair man wants to rob you, he'll do it when he's writing the bill.
Good One!
TRUE..the repairman was looking to see if there were males in the household or someone else
who might know he was gouging you when he did the repairs and billed
you. i know LOTS of trades repair companies (especially plumbers and
heater/AC) that permit their installers to keep half of the take.
their crooked tradesmen will look around to gauge the ability of the
customer to call BS on unnecessary or bogus repairs...especially on
women who are unlikely to know if there even is such a thing as a
conibbler pin or a fragistat. years ago my wife got a bid for $750 for
new brake pads on a small car. when i called the guy to ask if that
included the rears and new rotors and bearing he said no...JUST PADS,
front only...no fluid bleed, no bearing regrease, not even a rotor
resurfacing. i told him he should be ashamed of himself as i had a bid
from the local legit repair shop for $130 including surfacing, repair
persons are incentivized to overcharge but are smart enough to do it so
they don't get caught
Mortimer Snead He likes the way you decorate?
VALID POINT !
You should tell your wife to have her Veyron serviced somewhere else.
Great, explanation. Your real world examples were very useful for me to think through. Thanks.
Think more as wise as possible the hardest way when I learnt how to trust none when everyone doubted or confused me...
Vs
Think more when I learnt how not to trust to those whom I trusted either when they make fun about me
Most people are really good at "Biasian" thinking.
genius pun ... duh
I see what you did there.
...which is to say, really good at fear mongering and mystical belief.
But they have to weigh up how true it is first.
bahaha i love puns. really helps that its spelled out lol
The fact that none of those stories were completed shakes me to my core.
I wanna know wtf the repairman was doing because I peek around a lot and i dont have a lot of social experience, so i like to know what things people are doing wrong
Ikr?
Think more to not be fool either by how others testedly testing my way of knowledge perceiving life...
Vs
Think more just like I know what my hands did in an hour, a day, a week, a month, a year and how I bestowed on the outcome of it regularly
Think more when I know what's the right thing if you show your dissatisfied about me...
Vs
Think more if you don't wanted me to hide anything from you
Julia I'm guessing you're the math PhD because I would have just straight up asked Tom what his major is.
maeve main?
NOT BAD
damn maeve mains every where
lol
i didn't know people still played paladins lol
I have absolute no idea why this was recommended to me but here’s a new subscriber.
If the algorithm recommended it, think of it as good fortune. If it was a friend's recommendation then maybe it was a hint to be more open minded?
Yep
Think like me who doesn't fall in love to you, but who never allow you to be in love with anybody...
Vs
Think like I still sense some emotional gamblers trying to snatching you from me
Very informative and probably useful as an introduction. Neat presentation, especially the graphics.
Think more the hardest way of how I abstract the point of view, that instinct traits of most of us elaborated the different perceives...
Vs
Think more as wise as how I become personally persuasive by not forcing anyone in what I believe, as the system wish
The fact that there's so many comments here along the lines of "wow, this totally changed my perspective on everything" is quite unsettling to be honest.
But positive.
Didn't find any, and that's unsettling too
well, It is reflected in the politicians most people choose.
ok why did a bunch of people get this video in their feed... pls comment.. what did u last watch?
@@sasisarath8675 "How to rob people by pretending to be a repairman"
Repairman snooping around for the circuit breaker: Appliance repairmen sometimes have this weird preoccupation with turning off the electricity to an appliance before they work on it. 220 volts can really ruin your day.
In the UK at least, by law there has to be a circuit breaker within reach of the stove. In the US it will be split phase, so pretty hard to get the full 220v.
@@Tensquaremetreworkshop Most stove are run on 220V as well as electric dryers. Fools and high voltages can soon be connected.
Maybe he was looking for a bathroom.
@@walkergarya Yes, I know. And that is split phase, so 110 to ground. If you are not familiar with split phase, look it up.
It's not the VOLTAGE that kills you, it's the cardiac arrest.
Think more as wise as how I stopped here
Vs
Think more as wise as how I understandably win a particular argument with you
Think more when I'm wise enough to be more than being busy...
Vs
Think more when I'm wise enough to not be fool by entertaining hardworking people
_sees repairman checking out my bedroom_
_slams him against the wall_
"8% chance you're gonna rob the place, huh punk?"
"but sir, I'm here to repair your bed"
"Bayes would disagree .... get out before I call the police"
That would mean there's a 92 percent chance you're just an a-hole ; )
for some reason, the 'but sir' immediately made the repairman British in my internal narrative, making your story even more absurd, thank you sir!
Odds are he either likes your house, or is shocked to disbelief at the mess!
I just read:
sees repairman checking out my bedroom
slams him against the wall
1% chance this is an adult film
Why is "Bayes would disagree" both the toughest and nerdiest line at the same time.
I've done a lot of repair work, and I know what's it's like to be in the category: "looks like he's going to rob you but really he's just doing his job." Let me tell you - every place is built differently, and you should always keep your eyes open.. One time I found a gas line going into a bedroom and not even capped off. The place would have filled up with explosives at the turn of a knob, well if not for my "snooping about" that is. But it's also part of the job description to not freak people out. I just said, "I need to look around a bit to make sure I know where all the gas lines are going."
That girl did not provide adequate background on stove repair. Like, old house, gas or electic stove. Why is this critical information? A good repair-man/woman, would look around to not only fix the point but also all connected to that point. Also, it would be so easy to inquire, why are you looking into bedroom/s? She phrases it snooping, which is secretly done, which did not seem to the situation/
Uh, I think that might have been because the video wasn't about stove repair. The details are rather incidental to what she was actually explaining.
She's in her thirties.
As a repairman also, I'll throw in my 2 cents worth. When you enter a house to do repairs you should always examine your surroundings to identify any potential exit points or hidden dangers such as friendly dogs that don't bite (been bitten twice).
Brew Sauce+ I've done a lot of electrical repair work, and it becomes second nature when entering an unfamiliar place to glance around looking for potential problems, to a point where one may not even be aware of it. And btw, I've spotted many problems -- shock and/or fire hazards -- that the homeowner was oblivious to. It is the responsibility of the electrician to spot these hazards, point them out, and recommend (even insist) appropriate remedies. I imagine it's the same for someone coming to repair your gas range (assuming it is a gas range). He would want to know if there any other gas appliances in the house, any lines/valves/couplings that might be problem, etc. It would be irresponsible to not ascertain this info.
You are a naturally gifted teacher, thank you very much. This will come in useful for certain areas of interest, in particular biases. If you've not covered Henry George yet, go down that rabbit hole and you may just find something.
This was exactly what i was searching for. Thanks Julia!
You are a naturally gifted teacher, thank you very much. This will come in useful for certain areas of interest, in particular biases. If you've not covered Henry George yet, go down that rabbit hole and you may just find something.
Good. I've "known" Bayes' rule for 50 years but your explanation was the best visual one I've seen. I like the way you apply it to everyday life. Thank you.
The trouble with updating beliefs while encountering new evidence today is we can all find evidence to support any belief. It really depends where one looks for said evidence. We all have so many information sources to tap now. So everyone can easily find whatever echo chamber they need, to reinforce whatever belief they hold dear.
Your statement is fully correct. It looks that statistics become more stable if you get more and more data. However the quality of data matters a lot too! And this is also included to the Bayes theory! The simplest example is having two Gaussian distributions, if you put them together, the tighter one will win, i.e. the more uncertain one has little impact. Indeed it is hard to quantify everything, but with the Bayes theory all is combined at least in a consistent way. If you want to get on something, the theory helps you not to loose.
Yes, you have to be honestly self aware to be able to use the principle - ie you have to ask the question "how would the data look in my personal echo chamber if I was wrong" vs "how would the data look in my personal echo chamber if I was right"? And you would honestly have to draw the conclusion that my echo chamber will still only resound the message I already have taken as true, wether my belief is true or not.
Think more when I can't sleep
Vs
Think more the only person I feel secured to tell to
Think more when I'm wise enough to stick with treasure....
Vs
Think more it doesn't mean I can be easily fool by those who die-hardly tried to teach me morally lesson
As someone who uses Bayesian systems professionally, in daily life thinking, and also to show why other people's arguments don't land, I have to say that this is a fantastic video. It very clearly illustrates to the layperson why Bayes is what is and what the messages are. I will be sharing this with others.
Let me guess, you're one of those geniuses that predicted that there was no way for Donald Trump to win? because after all, Hillary got the women vote, the latino vote...lol
Let me guess, you're one of those people that mocks people a lot and ends their sentences in...lol
I've often seen Bayesian analysis in the title of academic papers, and this explained the basic principle. But instead of offering five very similar examples, perhaps she could have moved on to some more advanced applications in scientific inquiry and statistics.
_"As someone who uses Bayesian systems professionally"_
It's funny, because for people with any amount of intelligence these kinds of methods would just be completely intuitive, obvious or logical when working out decisions, it's incredibly basic mathematics. But then I guess I should never be surprised by how low the bar can be.
+jamma246
If you think this sort of thinking is intuitive, then you might want to check out LessWrong.com so you can see how deep the rabbit hole goes. Fallacious and biased reasoning is the norm in 98% of the population. Most humans are extremely weak at rationality by default. This makes the world a rather frustrating place.
Four years since I first watched this video and for some reason, it is #1 on my recommendations today. Much appreciation. Watching this is bringing back fond memories of a summer long gone.
woah, that's SO strange because the same happened to me!
I got recommended this video and the thumbnail gave me de ja vu, because I've seen it before. And I think it was four years ago as well.
I've noticed a lot of comments dated "2 weeks ago". Maybe this youtube channel is making a big comeback.
Think more when I learnt how to be busy instead of how to be sexy
Vs
Think more when I learnt how to be sensitive instead of how to be sensual
Think more it's the only reason to have a strong argument with what I stand...
Vs
Think more as wise as possible it's the hardest way to evaluate life as scout mindset
I realize I've been using this intuitively for years to fight my, or others' fears. But being able to quantify and codeify it is such work work of brilliance, I'm astounded. That's a smart person.
I have wondered what happened to Tom, he was my first friend on MySpace.
tchrisou812 oh Tom
Have you got him locked in your basement?
Tom is in the unemployment line.
He was my only friend on MySpace
Here I is
Think more the hardest way when I'm wise to be protective as mother to father, as father to mother...
Vs
Think more although most of the time they complain to each other
Think more when I'm wise enough to stick with the last updating photos...
Vs
Think more when I cannot be fool like I wasted my day as Social media addicters
I never update my priors.
In fact I would have assumed the repairman was wondering where he was gonna lay me out after eating my liver with some fava beans and a nice chianti.
Fake repairman is the oldest cannibal trick in the book.
which is why you're still here to tell the tale ...she's trying to lead us astray ...thank you
I just phone for a pizza delivery -guy-
That's seems like adaptive bias, where we adapt to minimize the cost instead of the actual probability
i laughed out loud at this
I like a nice Chianti. Am I a cannibal? D:
These personal experience examples were amazing, helped understand it more intuitively. Thank you! Came here after crunching through some equations but these real world examples showcased the theorem in a very simple way.
How do we make balanced/accurate estimates for the figures used in the Bayesian reasoning framework?
Think more the hardest way to fool not by the unsuccessful challengers
Vs
Think more as wise as how I trusted my deep rooted instincts
I had a rudimentary understanding of Bayes theorem prior to this video, but now I feel like I really understand it. thank you
I've always liked to use something close to this general thought to keep my analysis, general guesses and knowledge of stuff updated and changing, avoiding fixed preconceptions or prejudices. This is quite similar in many ways to my personal system, although I haven't put it down in numbers or created clear rules and patterns, it was more psychological and simple.
It's very interesting to find something close, and makes me even more interested in the possibility of studying statistics, something I already like a lot, but don't know if I like enough to live on it.
Thanks for this, I think I first saw you with Matt Parker on Bayes. Keep up the great job. Every detail can have a small influence on coming to momentary (?) conclusions, always doubt yourself.
Think more when I learnt how to be wise enough as an outsider....
Vs
Think more when I learnt how not to fit in to escape hell
Think more the hardest way as wise as how I'm honest to myself, with every details of how I spend my precious seconds of every minutes of every hours....
Vs
Think more the hardest way even when I was supposed to be happy in a framely set-up man-made time-line schedule
Got a good chuckle out of the mathematician joke actually.
+Daniel Korolev that was good joke
Couldn't help smiling when I head the words 'Berkley' and 'snowflake' in the video. Hard to imagine extremely intelligent people becoming snowflakes. But may be there is no correlation between intelligence and wisdom.
Not saying the presenter is a snowflake. But I see a lot of young people take positions that would be considered 'progressive' in their eagerness to 'look' elite among their peers.
+B-Rad that's exactly what I am talking about - Classic elitism. I should have also added that this behavior has to do with conforming with 'views' spread by the progressives elites, so one could look like them. It is implied in my statement, but seems some people need more clarification.
Let me guess, you 'think' to care about animals & environment means to not eat them, because you have 'learned' this info from material that you read or watched on T.V or the internet. If you tell me you have a psychological problem to kill and eat another living, breathing thing, I will probably excuse you. But, the loving animals and earth etc is baloney. You just don't realize it is baloney - that's all.
If I prove to you that vegetables and plants also perceive pain..... my bad, this has already been proven. (Read about scientist Bose's work from more than a 100 years ago) Will you stop eating food altogether?
Those studies which claimed to prove that plants experience pain have been debunked. It's not true.
sez who sbunny ?
Wow! This was very insightful. Even the way you calculated the conditional probability without using the formula and just using the areas instead.
Think more as wise as possible to not be discourage when everyone says bad things on my back
Vs
Think more as wise as possible to learn how to finish my own scheduled duty in a day and bother not with everybody else's businesses
Isn't it amazing how personality and the subsequent psychology factors into not only the type of career path one may choose to do but also their attitude in life? Some people naturally tend to be shy while others are predisposed to be extroverted and thereby inclined to have greater degree of social success - these are the business and management types and are often well suited to their role. Perhaps this could be taken as an indication of what career an individual might be better suited for rather than lumping everyone into a uniform set and expecting them to perform in an identical way in accordance akin to a one dimensional academic expectation. Its like throwing out the baby with the bath water. In education, many will display a greater inclination toward a specific interest that presents itself as a good reflection of what they are really curious about. These subsequently aspire toward achievement in their chosen fields that is often associated with quiet study and solitude (think library) often resulting in an excellence in both attitude and performance. Additionally however, such a generalized performance model or KPI can exclude an individual from achieving their true potential as the expectation is in accordance to a generalization rather than specialization.
What would the personality traits of someone have to be for you to suggest they become a career criminal?
Bayes' Rule is an important component of critical thinking. The ability to think critically is a skill that needs to be learned. The challenge is that common sense and intuition are often very wrong, and there's no trivial way for knowing when. It's on a case-by-case basis, and all those cases are about patterns that need to be recognized and examined.
I was reading an old newspaper and came across this theorem, thank you for clarifying!
why were you reading an old newspaper?
I got an odd sense of deja vu while reading your comment.🤔
do you even know what a theorem is?
Old newspaper? As in, RUclips would only play at 480p in it?
Ever in your life did you wish you had a Hurdy Gurdy?
Think more as wise with 98 minutes ago since 03:00 PM
Vs
Think more as wise as how I stopped having evening refreshment tea and lunch at home, yet with a somehow little effort I managed to cut the grasses as I was assigned to
A very simply rule to check your prejudice and update the belief system.
Your videos have added that extra weight to my priors I need to convince me of the merit of Bayes Theorem. I'm committing myself to practice Bayes thinking. Thank you!
My friend; Bayes Theorem is running and operating regardless of your commitment status. To me, the video is a statement and not a proposal.
@@gyrojomo
Your perspective is of equal relevance to me, a 3rd party stranger. And perhaps OP's statement can nudge one more person into accepting the rationally sound choice of incorporating Bayes Theorem into their lives. That is a non-trivial post, but yours seems negatively intended and leaves me wondering, for what purpose?
This seems like a good way to justify your position while also being wrong. I like it.
Late to the party, but best comment. This is Bayesian Feelings. Even got the formula wrong.
maybe he was just nosey, it sounds like an episode of law and order
Maybe he's in the middle of designing a new house/decorating ... bottom line, assume nothing. At the same time though, trust no one ... ...
I had the same thought when she mentioned meditation. How can sitting down and doing nothing be 'fake'? More like 'I dont have what it takes to do it, so I'm gonna call it fake to convince myself it doesn't work'
Why would you like something that encourages falsity and error? Are your feelings more important than discerning the truth (which is the basis for this whole video)?
Think more the hardest way as a person who always managed to complete the task with deadline...
Vs
Think more the hardest way to not be fool by the delayers' tactics
Think more even if I had nothing in mind to say...
Vs
Think more yet I can't be repeatedly fool like I still have times to happy with others when I'm actually not for one reason
Another important clue that Tom is a Math PhD student: He's walking. MBA students travel around campus in golf carts that they stole from the campus maintenance department.
Exactly.
Remember your priors!
remember your priors, how likely is it that a math PhD has the courage to venture outside of their room and into the savage social environment of the campus
Never did think of Bayes Theorem as a way of life, but it does seem fun.
@Julia very good explanation. What is the tool you used to draw the things on screen?
Think more the hardest way to fool not by alternative secrets of the miraculous appearers
Vs
Think more as wise as how I didn't appreciate the everything comes in one tactics
The willingness or openness to challenge your initial impressions, and subsequently alter them, is a component of the attribute we used to call "humility". It has more to do with wanting to see things accurately, than it does with some false sense of being humble.
This is such an amazing explanation. Thank you so much!
Think more as wise as possible with Computing W is for Wide Area Network...
Vs
Think more as wise as possible with Computing X is for Xperia
great vid. What's the joint probability prior of shifty eye repairmen?
This is one of those rare things which feels like a bug fix to the brain
machiavellian thinking is far superior to this crap
Rare? Mate, all I fucking do is troubleshoot this buggy piece of shit.
@@creamwobbly tomayto tomato
@@LowerYourExpectationsPleb what are you on about, those two don’t even have to exclude each other
It was the 'university campus' bit that got me. If you'd said 'federal prison' it would have been perfectly obvious.
Think more the hardest way to satisfy not only at the level of how others perceived me morally...
Vs
Think more the hardest way about how I believed in the positiveness of why I didn't have to agree with all they elaborated their point of views
Think more as I grow old...
Vs
Think more as automatically regretter once I came across and encountered with stuffs that makes me Reasonable regarding with our daily behaviours
I can't believe I took so long to find this channel.
a similar method I've used since I read about it in childhood: when the Wright brothers were debating methodologies they'd switch positions and argue for the other idea on the table. it's also a great tool just for building empathy and considering viewpoints that you don't currently, natively inhabit.
I would assign a high probability that Tom is on the Autistic Spectrum (based on his behavior and my experience with people on the Spectrum), which would add to my confidence that he's a math student because I have noticed a high proportion of ASD persons tend to excel at math but have little interest in business.
Very good video. I m learning statistics and this has helped me a lot
I couldn't help being distracted by that light switch just left of your head, so . . .
Bayesian thinking:
1. By your accent, you are probably American filming this in the USA.
2. Common US building code makes the top of the light switch about 4' high.
3. By making a quick judgement call, if you were standing up for this video your height would be about four foot, three inches.
4. By my experience the percent of adult women in the US who are only that tall is less than 1%.
5. I am adjusting my perception of you standing in front of a wall to perceiving you seated in a normal chair talking to a camera on a tripod.
Okay, I am subscribing to your channel.
Maybe the light switch is just low down.
That is just in your head Scott. She just wants to explain things right in the video. And she does. There isn’t any more to this video.
Spot on. Very insightful.
Hey Scott: what percentage of women's garments are low cut? Have a look around the stores, I'll wait.
@sk54931 Perfect height for a woman that is, yes.
That math joke was pretty funny lmfao
If anyone did think that Bayes Rule *was* the be-all-and-end-all of ways of thinking, then wouldn't that mean they don't understand Bayes Rule?
Think more as ownership secrets..
Vs
Think more to fool not by acclaimers tactics
I've never thought that my constant complaining about people implied to them that I was jealous lmao
For sure a reasonable percentage of people who know you have come to that conclusion.
i joke about this a lot but that doesnt mean i believe people are actually jealous of me
The virgin math PhD vs. the Chad Business major.
If I had a PhD in maths I wouldn't care about being a virgin tbh. That wins every dick measuring contest anyways.
@@MrCmon113 The virgins are evolving.
Actually math PhD makes hella more money than business major
lol i was afraid to find comment
@@rephaelreyes8552 Yeah that's why mathematicians have all the private jets, super cars, and hundred foot yachts, and they get aaaaalllllllll the bitches.
LOL shut the fuck up.
Great video! What is the software used to create those images?
Think more the hardest way, since 25 minutes ago with musical tracks that suit a mood of a day, less with relaxed cafe tune I listened a moment before my lunch, less as a 1500g of potatoes I forgot to mention that I picked from eldest brother this morning, less with the old lady who walked in the house compound, the hardworking gate rigid plasterer, the hard working clothwashing maid, the uncle's son who recently showed-up, the house-room floor washing sister, the neighbour garden owner....
Vs
Think more the hardest way as album reeling film photo of 2005-2008
What kind of watch is Thom wearing? Is he wearing a vintage Casio calculator watch from 1985?
As to the final part, "Update incrementally", it is good to keep in mind when doing so that forming a general principle based on personal exposure, even if to many adherents, is still anecdotal not empirical, and thus influenced by the persons own biases or the context of the social norms. So in Berkley, where there is a lot of new-agey sentiment there are more people who feel that meditation is beneficial and this in and of itself can increase ones own personal perception of benefits, or if formulating opinions based on informal tallies of personal interactions, lead you to think, well it must actually have positive benefits because so many of those I encounter say it does. It is much like if you went to Brigham Young you would find many more people who said that prayer caused changes in the world or if you were at a Rainbow Gathering you would find a high percentage of people who felt LSD expanded your mental abilities and capacities.
Well said! That incremental exposure to an idea is how advertising works. One would be better off to let the positive words from a respected friend lead them to research the scientific evidence of the changes that, in this case, meditation makes in the brain as shown in brain imaging/scanning..
Excellent video. Really makes the theory understandable.
Think more the hardest way as how a pile of *Grasshopper* looks like when we cooked them with simple method by attached them in proper arrange on a bamboo piece
Vs
Think more as the gold color appearance when they are perfect for having them
Think more to always go with the flow...
Vs
Think more yet not to always be over-confident
I don't know much about meditation, but as far as I do know, meditation is nothing more than you practicing to control your racing thoughts. And as we all may know, the more you practice something, the better you get at it.
@Fernando Cunha I'd actually say that it is incredibly simple once you get the hang of it. What could be simpler than winding down? I've done it for 10 years and I love it.
I'd also just say that it is more about being attentive and open to yourself than about actually wanting to controlling your thoughts, though it's true they will become calmer and more focused.
I would agree however, that without some practice in a meditation centre under a proper teacher it can be difficult to get the hang of it by yourself.
I highly recommend the books and talks (a lot of them are in youtube) by Thich Nhat Hanh (vietnamese zen master). He speaks plainly and powerfully, in a way akin to science. He likens zen theory to Lavoisier's principle of the conservation of mass. And you can feel that he is largely free from attachment and dogma.
Man I can't wait for this to be implemented in the next patch.
Think more the hardest way with some common backup tools available in the market such as
•Backup Home, •Auto back-up, •Taskzip, •Backup Platinum etc...
Vs
Think more the hardest way as how several methods for data backup can be included such as Full Backup, Incremental Backup, Online Backup, Drive Imaging etc
Think more as wise as how I know my level of mature concern comes out when nobody taught me...
Vs
Think more as wise as how I know that picking up some strange ideas from others just turned me not as concerner but as confuser
This is great, particularly the animation of updating your priors after receiving new information like in the meditation example. Most people only update their priors when they get a result that confirms their previous bias.
I reluctantly agree. And I perceive that social media, with its stovepiping algorithms, exacerbates this. One can, almost without noticing, end up in silos where there is a high degree of conformity of opinion, and where differing views are subtly, or not so subtly, marginalized.
In my own case...though I try to avoid confirmation bias, I have no doubt that I'm afflicted with it. It's easy, maybe even comforting, to be surrounded by people who agree with you, and to latch on to tidbits of info that confirm one's vested position. OTOH, when I re-think a position, based on new evidence, or even a compelling personal testimony or someone eloquently putting forth a different view, it feels liberating.
But remember, she has the scout mindset (and not the soldier mindset) !
Problem #1: When an accident happens, what is the probability that the accident is caused by a bad driver, given that:
1) 90% of the population has been involved in at least one accident
2) 30% of the population are bad drivers (means 70% are good drivers)
3) 99% of the bad drivers are involved in at least one accident
P(Bad Driver) = 0.3
p(Accident|Bad Driver) = probability of a bad driver causing an accident = 0.99
P(Accident) = 0.9
P(Bad Driver|Accident) = probability of an accident caused by a bad driver
= 0.99 * 0.3 / 0.9 = 0.33
= 33%
When an accident happens, there is only 33% chance that the accident is caused by a bad driver.
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Problem #2: Find the chance of having cancer, given that the customer is 65 years old.
Facts:
(a) 1% of the population have cancer (99% don't have cancer)
(b) 0.2% of the population is 65 years old
(c) Of those that have cancer, 0.5% of them are 65 years old
P(Cancer) = 0.01
P(65 yr old) = 0.002
P(65 yr old | Cancer) = 0.005
P(Cancer | 65 yr old) = What percent of the 65 year old population is likely to have cancer
= P (65 yr old | Cancer ) * P (Cancer) / P(65 yr old)
= 0.005 * 0.01 /0.002
= 0.025
Only 2.5% of the 65 year old population is likely to have cancer.
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Problem #3: Given the following:
(a) 1% of the population have breast cancer (99% don't)
(b) 80% of the mammograms detect breast cancer (20% don't)
(c) 9.6% of the mammograms detect breast cancer when it's not there (90.4% of the tests correctly return a negative result).
You have got a positive result.What are the chances that you have breast cancer?
P(Breast Cancer|Positive Result) is what we have to find.
P(Breast Cancer) = 0.01
P(Positive Result|Breast Cancer) = 0.8
P(Positive Result) = We need to consider both positive and false positive
= Positive + False Positive
= You have breast cancer and you have been correctly identified as having breast cancer + You don't have breast cancer but have been identified as having breast cancer
= 0.01 * 0.8 + 0.99 * 0.096
= 0.10304
P(Breast Cancer|Positive Result) = 0.8 * 0.01 / 0.10304
= 0.0776
So, if you have a positive result, there is only 7.76% that you have breast cancer.
Problem #4: Spam detection
(a) 50% of the emails are spam
(b) Out of 1000 spam emails, 110 contain the word 'Nigeria'
(c) Out of 1000 non spam emails, 48 contain the word 'Nigeria'
A message with the word 'Nigeria' arrives in your inbox. What are the chances that this message is spam?
P(Spam|Nigeria) is what we have to find.
P(Spam) = 0.5
P(Nigeria|Spam) = 0.11
P(Nigeria) = Probability of a message having the word 'Nigeria'
= Probability of word 'Nigeria' appearing in a spam email + Probability of 'Nigeria' appearing in an non spam email
= 0.11 * 0.5 + 0.048 * 0.5 = 0.079
P(Spam|Nigeria) = P(Nigeria|Spam) * P(Spam) / P(Nigeria)
= 0.11 * 0.5 / 0.079
= 0.69620
There is a 69.2% chance that the message containing 'Nigeria' is a spam.
Clever. There is a 99% chance you are a mathematician but since I am not, my view of probability and judgement is skewed.
xazzbi Yes, just draw the rectangles as in the video. Instead of Math/Business you have cancer/no cancer, and instead of shy you have "positive result".
P(Cancer) * P(65 yr old | Cancer ) represents the Probability that someone you know nothing about has cancer AND is 65 years old (first you take P(Cancer) since you know nothing about that person and then you multiply P(65 | cancer) since the cancer part is already included in the first probability).
Now you have the "pool" of people who are both. But since you know (in the problem) that the relevant portion is 65 years old you have to divide by that probability to include that knowledge.
Proof (I know it's not helping to visualize :P):
P(Cancer) * P(65 | Cancer) = P(65&Cancer) = P(65) * P(Cancer | 65)
P(Cancer | 65) = P(65&Cancer)/P(65) = P(Cancer) * P(65 | Cancer) / P(65)
It should be noted that the conclusion of problem #3 only applies if you randomly test people from the population. If you were prescribed a mammogram to begin with, there are other reasons why your physician suspects you might have cancer, and therefore belong to a population that, even before testing, has a chance of having cancer higher than 1%. Also, is your figure of 9.6% of false positives a real one or did you make it up?
Think more as wise as possible after completing another meal of a day before 12:16 PM
Vs
Think more as wise as possible the hardest way to believe not in some strange stories that anybody somehow managed to fool during lunch, breakfast, tea or dinner time
Think more as wise till 11:50 PM
Vs
Think more as wise the moment I'm curious about you, the moment I know that life is completely complicated and full of doubts
This popped up in my recommendations. Never have I been so instantly hooked.
Damn. You're a good teacher, I actually learned something.
Think more the hardest way as how the journey of Hindi Journalism began on 30 May 1826 from Calcutta with the first issue of *Uddant Martant* under the editorship of *Pandit Jugal Kishore Shukla*
Vs
Think more the hardest way as how Jugal Kishore Shukla was known as an excellent editor and had mastery on many languages including English, Bengali, Urdu and Persian...
Think more as wise as possible to figure out what I miss
Vs
Think more as wise as possible to figure out why I shouldn't be dismiss
based on this video i am going to predict you will make more videos with light switches in background
hilarious, was laughing for 2min :DDD
Right on. I can only remember this talk as the Light Switch Theorem
Your 'prior' that the switches are majorly for lights needs to be updated.
I've been struggling to "get" bayesian stats for a couple of years, sorry to say, because even in my technical work (biomedical informatics) I need visual representations of abstract relationships to help me think through problems. So your visual aids were extremely helpful to me. They took a rather wobbly abstract concept of priors and offloaded them to a visual concrete representation to reduce cognitive load. Thanks so much and I've subscribed to see what else I can learn!
To me, it's a cognitive load even after visual representations. One is either numerically/scientifically predisposed or isn't. I don't think you can force yourself to become adept at something you're not naturally adept at.
Think more the wisest way back to where I stopped last night with *Communication Dynamics* on *Do you Understand* ?
Vs
Think more the wisest way how I should *Ask myself, as a communicator, "Am I clear in my own mind about what I'm trying to say to others?"*
This is really nice way to convey how statistics can be fallable and misunderstood
not to mention how they are purposefully misrepresented in propa pieces, being reported as percentages without absolute numbers and vice versa..
This reminds me of a Government ad I used to hear on the need to wear seatbelts. It basically said you need to wear your seatbelt even on short trips close to home because something over 50% of all accidents happen within 5 miles of home. And, well, duh. 99% of all miles traveled in cars is within 5 miles of home. Anyway, 87.32% of all statistics are made up on the spot.
puff puff give willie
I think it makes sense though, if people are not wearing their seat belt because they think that since it's just a short trip they don't need to. So, it is countering an inappropriate instinct. Because maybe people don't think about the cumulative distance they are travelling in short trips.
yeah on the spot, just like you made up 87.32
@@rohithipparkar707 That's the joke.
Steven Wright once quipped “Someone told me half of all car accidents happen within a mile of your house. So I moved.”
I think people should learn Bayesian from its statistical development. Bayesian method in psychology is just scratch the surface.
Sources?
Think more the hardest way with the same anointed computer mouse clicked hand that I communicatedly reached out to you with the flow of highly expressive commenting
Vs
Think more the hardest way when it's though for the readers to understand how I combat my normal mind
Think more the hardest way as how the human emotions, ideas and thoughts are in the form of psychic image and they have to be first converted into signs capable of being articulate in the form of speech which is later encoded into different kinds of signals like radio waves or script depending upon the medium one wants to use
Vs
Think more the hardest way as the encoding and decoding on further analysis become even more complex when the factors like individual's personal experience and the social hierarchy and sub cultures are included in the process