Are you Bayesian or Frequentist? 

I love this subject! I'm studying Bayesian methods in my PhD, here's my perspective: Frequentist reasoning wants to deal objectively with data, so it considers probability to be a property of the world; it says "the coin has probability 1/2 of being heads because that's the frequency of heads in the behavior of this coin"... and there's a right probability, it's a fact from the world, it can be learned by data that shows that frequency in behavior. Data is noisy, but it reveals true propensities through frequencies. Bayesian reasoning wants to deal logically with data, so it considers probability to be a property of logical propositions about the world; it says "the statement 'coin landed heads' has a certain probability of being true, it is 1/2 for me and 0 or 1 for you depending on what you see"... the proposition is connected to a point of view, and different points of view will differ in how close they are to the truth about the state of the coin. So probability is subjective in a sense, but all points of view with equal information should objectively agree about probabilities of their statements (it's objectively subjective, just recognizing the existence of different points of view, but they are not supposed to be personal, not opinions). When you update your "belief" over data, it's because data moved your point of view in relation to the "truth". In this example, once we see the coin, we update the statement "coin landed heads" from 1/2 to 0 or 1 depending on what we see (probabilities of 0 and 1 mean perfect information while 1/2 means no information). There isn't an actual divide between the two, theoretically... Bayesian reasoning recognizes the relation between frequency and plausibility, while frequentist reasoning recognizes points of view, it just doesn't go there.

As a psychiatrist, I feel like I rely on both Bayesian and Frequentist philosophies in my everyday work. When advising on diagnoses, I use the Bayesian approach. That is, I gather whatever data I can to inform an opinion (about a diagnosis), and then I update my opinion if and when more data emerges. I'm not overly invested in getting a 'right' diagnosis because a patient's presentation is dynamic and complex such that they can't always be reduced to a single category at all times. I'm happy to revise the diagnosis when necessary. But when I'm advising on risks (i.e. the risk of somebody committing suicide, homicide, arson, etc.), I use the Frequentist approach. I am infinitely more concerned about what will happen when a patient has had numerous repeated attempts at harming themselves or others because that informs the probability of how likely a person is going to repeat history. I think to myself, "what will happen if the patient attempts the same move another 100 times?" To me (and I'm not a statistician, although I know a little about human psychology), the Bayesian and Frequentist approaches are fundamentally concerned with certainty vs uncertainty. The Bayesian aligns herself with changeable opinions informed by available data, thus she is never completely 'certain' about anything since her opinions change when new data emerges. The Frequentist on the hand aligns himself with unchangeable facts based on logic, thus he is always completely 'certain' about everything as long as his logic holds water. The coin toss was a great teaching example. It was a great example because the answer was inconsequential. I mean... Who cares how the coin lands? Nobody was harmed in the making of the video, yes? (I hope). We can allow ourselves to assign equal weight to both philosophies in this teaching scenario when the outcome of the coin toss was inconsequential. I suspect people are likely to gravitate towards a Frequentist approach when contemplating decisions that are very consequential because the Frequentist approach feels more tangible to me while the Bayesian approach feels more abstract. So I don't think it is a matter of 'are you a Bayesian at heart or are you a Frequentist?' Rather, it may depend on the weight of the decision you are about to make. Having said that, I do acknowledge that some people are more tolerant of uncertainty than others, thus for those people, they are more likely to be Bayesian perhaps. Does this make sense?

LOL. Schroedinger's coin.

I think it has a lot to do with the nature of the question and the search-space in your problem, rather than your personal choice, to go with a frequentist vs bayesian method.

I don't think the framing of Frequentists caring about the true answer is a good one. Bayesians and Frequentists both care about truth, they just care about the true answer to different questions. I think the main difference is that Bayesians and Frequentists ask different questions, and use language that implies the questions they care about, which is what makes it so difficult to have a conversation with the other perspective. When truly asking the same question, the two mindsets should converge on the same answer.

“The truth has already been fixed in the universe”. Powerful, powerful stuff. 🙏

Two minutes in to my first Cassie Kozyrkov video and I'm subscribed.

49% heads. - 49% tails - 0.4% a bird steals it - 0.4% it disappears - 0.2% I’m imagining this and it doesn’t exist (but my eyes construct the visual spectrum in my mind)

Thank You.. You are a seriously great teacher, I'd like to see your videos as a necessary part of every high school students curriculum. You remove the jargon and re-frame the learning references to simple, understandable examples which makes the learning of complex issues so much easier.

Thanks for summarizing this important topic. I've no emotional investment in the Frequentist vs Bayesian debate (I've used both often in my research), but I couldn't help but feel the Bayesian perspective was not given fair credit here. The Bayesian's "point of view" should not be entirely subjective, but rather based on logical principles, that can often be derived from the laws of nature (eg. The shape and symmetry of the coin make it equiprobable to land on heads or tails). The powerful advantage of leveraging prior information for forecasting or evaluating hypotheses also ought to be emphasized more. Ideally, aspects of both Bayes theorem and frequencies should be used (eg. using base rates as prior information in diagnostics). But because the frequentist approach is so much more intuitive to use in science, the Bayesian approach is underutilized. This has been less than optimal for science which has been far too dogmatic about p-values instead. It would be nice if you could emphasize this more in future communications on this topic, thanks!

Thank you. Perfect pausing during the presentation. It is so rare among RU-vid presenters.

Gracias Ms Cassie. Very well explained. Thanks to YT recommendations as well

This is AMAZING!! Great video. Thanks for sharing!!!

Hands down the best video I’ve watched on the philosophy behind both the Bayesian and Frequentist approach. Well done

How is it possible that I only found this channel now? This stuff is brain-food-candy for any statistician like me! Keep it up :)

Cassie, thank you for detailed explanation. Please, please, please tell us more about pros and cons of Bayesian vs Frequentist approaches in the business context.

I love how you explained the 2 perspectives.

I am binge watching your videos. Wish I’ve known you and your work before.

What a beautiful philosophical view statistic perspective. Loved it!

Thank you for your clear explanation!

Frequentist: "What is the probability the actual current state of the coin is ..."? Bayesian: "What is the probability my estimate of the state of the coin is ..."? It seems Frequentists try to take an objective point of view. Meaning: from the perspective of the focal object. Whereas the Bayesians take a subjective view. Meaning: from the perspective of the subject/observer.

thank you for this EXCELLENT video!

I like the evolution of these videos into a nice variety of presentation.

This is a fantastic short explanation of the differences between them - thank you! Also, for some reason, you kind of remind me of Kes from Star Trek Voyager…

Excellent vídeo! Thanks for this explanation

Fascinating explanation, thank you

just came across this wonderful video, very simple explanation, read many articles but still confuse with the technical terminologies they have used in the paper. from this video within 5 minutes i have understood the concept. Thankyou Cassie for sharing wonderful knowledge with us. really appreciate it :)

I think it’s important to understand whether your need is action - doing or not doing something in the real world - or just thought/academic. Bayesian tends to promote action, such as our decision to drive more slowly in poor weather. Frequentist tends toward addressing issues where a discrete level of certainty has utility (often without action), such as hypothesis testing.

This was beautiful. Thank you.

It's curious to think about probability and statistics theories in physics. In my perspective, the experimental physicists generally goes with a Frequentist mind, since the common mindset is to try the same experiment over and over and look what percentage they got a "good answer". In the other hand , the theorists care too much about perspective and information, actually the quantum theory is bounded to theses concepts, hence, the resolutions of the problems are made from a Bayesian mind. Your videos are awesome! Loved it!

it occurs to me that most situations where you want to know a probability are Frequentist, i.e. they concern things that are already facts, but unknown to us. From a certain perspective *all* probabilities are Frequentist, if you accept that we live in a deterministic universe. All future tosses of the coin are already predetermined! Love this post!

I recommend reading the short paper Bayesian Estimation Supersedes the t Test.

Holy crap, statistics has a place for me. Never heard of Bayesian before. I gotta do some reading now. Thank you! Seriously, that makes so much sense in my world.

Beautifully put. Very intuitive.

Clear explanation, thanks. Will it be possible to have a mathematical explanation as well, such as doing the same analysis (for instance comparing mean across two groups) using Frequentist (a t-test) versus Bayesian approach (?) ?

It seems like it first depends on how a person understands the initial question. I understood it as what's the probability of me guessing if it was heads or tails. Answer is always going to be 50/50. The coin already landed so it was never a question of which way it was resting on your palm. That has already been determined. The only thing left to do is guess the right answer...which is always going to be 50/50. Edit: This was such a random video click for me. Lol.

I like how you paused after you the coin had landed and you were going over options... I was yelling there is no probability since it's a completion action. I guess I'm a frequentist. Thanks for teaching me something 😁 very good lesson!

*Neo* "Heads!" *Morpheus* - "What if I told you there was no coin...?"

And the Micheal Baysians don’t care I’d it’s heads or tails, as long as the camera orbits it.

Great video and explanation! :) By coincidence, I came up with the exact same example (covered coin toss) to explain the difference between Bayesian and frequentist to my colleagues, and I was also going to use it in a paper I‘m writing. I‘m wondering now, is there a „common source“ of the example that I should be citing?

I think both perspectives can be beneficial in different scenarios, depending on what you’re trying to accomplish.

Very well explained.

that was such a beautiful explanation

Loved it!! Theoretical chemist by profession, I daily have to navigate the thin line between the groups of people who either call themselves "Statistical mechanicians" or "Quantum mechanics". I might cite this video in future to demonstrate to my colleagues the philosophical difference between the two. :)

A better question is, would you go for Monte Carlo simulations or bootstrap draws for small samples 😉

1:00 I thought it was a trick question and you were going to show the coin stading up, stuck between your fingers, to make a point about how there might not be a probability. Guess that makes me a Bayesian.

This video, besides sprouting an interest in the philosophy of probability (to put it lightly) and how English sounds to those who don't speak it.

Well done!

This is really neat, thanks!

Hidden under your other hand or hidden in the future, is there a meaningful difference?

oh wow!! So helpful for me - thanks!!

In my undergraduate statistics courses, I essentially was indoctrinated to think in a frequentist way, to look for the result of a statistical experiment and say that I conclude with 95% confidence (or based on whatever your confidence level was) that a result was significant, or say that I have failed to reject the null hypothesis. So far, I still like that way of thinking.

You're a damn good teacher madame! If you are not using that talent somewhere along your path, then it's a crying shame!

If the coin is heads-up before tossing, it will always land heads-up, and vice-versa, IF it's landing on the palm of the person tossing the coin. If it's landing on hard surface, it can go anywhere due to the bounce / twist / turn of the coin multiple times before it comes to rest. So, which one am I?

Awesome video and great explanation! I came across a problem recently that seems like a mix of both philosophies but I can’t wrap my head around how to solve it! Let me tweak the problem to match your example. Let’s imagine that you made this video twice, in one you used a fair coin and in the other you used a biased coin. However, we, as the audience do not know which is which. How can we distinguish with

This is the coolest video I've seen in a while!

THANK YOU so much for this video, and all your videos. Please keep making them. I love to learn and appreciate great teachers. You accomplish both feats...and I don't think a Bayesian or Frequentist would disagree. But maybe they would. lol. Again, THANK YOU.

Amazing video!

I just stumbled across Florence Welch talking to me about statistics and I love this.

What if I went bayesian in the first question and frequentist on the second? On the third, I couldn't even choose. But I 100% subscribed, great video!

I’m curious. Say that I’m in the gym lifting a certain weight. With no more info, I won’t add weight, but if I measure the velocity it could suggest that I could add weight. The decision is binary, add or not add. I’ve thought that this is a good place for Bayesian to shine, letting me know the probability that I could lift x more weight. But your video makes me think that this binary decision leans more toward frequentist thinking. The underlying assumption in my specific example is that there is an inverse relationship between load lifted and the max velocity you can lift it.

Loved this!

This is why I’ll never understand statistics beyond mean and standard deviation.

Thank you!

awesome tutorial..

The Bayesian perspective reminds me very much of Schrödinger's cat experiment. :-)

This video gave me more questions than answers, I liked it

Thanks a lot!

I'm backing the superposition, where the superposition changes based on the likelihood that you were lying in the reveal, since the coin was too out of focus to tell what the result was.

That was the coolest thing I've seen this year.....I think....

Thanks!

I think I flipped back and forth while listening to you talk about the 2 ways of thinking. I think both ways have merit, but I believe that I lean towards Frequentist.

As a kid, I used to wonder what the space between the stove and the pot was called. As an adult, I had the same issue with frequentism, I just didn't know how to formulate the question.

Love this!

My own research is in electronic engineering and I teach a graduate course on Stochastic Processes to engineers and applied mathematicians. I do research with both statisticians and other engineers, and have thus develop a rather pragmatic view. Losely, I pick the perspective which helps my current project. This leads me to be Bayesian 50 % of the time and frequentist 50 % of the time. (And Iannoy 100 % of the statisticians most of the time... ) I do not think that you should or need to choose between the two views. I think that both views are correct - but it is not the same thing they are looking at! That is probability to a Bayesian models the current uncertanty about an event whereas to a frequentist it models a frequency of correct guesses if the experiment could be repeated. Incidentially, the underlying probability theory (the events, probability measures and all that) applies to both schools. But although the terms (e.g. Probability, expectation, etc) used are interpreted in fundamentally different ways. Many times the two views can lead to the same thing. I pick the view which seems the most helpful in achieving my goal in a certain application. A perhaps even more fundamental concern to have, is the view on probability theory itself. The "Are real things random or not?" questions. As a pragmatic engineer, actually, I do not care - what matters to me is that probabilistic models, are very good and convenient models for many phenomena. Applying statistics be it frequentist or Bayesian, lead to many good ways of guessing on phenomena which cannot be observed directly.

Great video! What are you recovering from as a statistician?

Statistical probability is a measure of ignorance, not certainty. Everything that Does happen always had a 100% chance of happening, we just didn't have enough information to know it. The two perspectives are perfectly compatible. Also, knowledge is justified belief.

Good explanation

what is the 'validity' of the question about probability of heads or tail once it is landed in your palm in this example is not clear ? what are its implications ?

Congrats Cassie! Your explanation is pretty good. I really appreciate your videos. 👏🏻👏🏻👏🏻

It’s the first time one has questioned it to me... great explanation!

I believe I cannot love this video enough. I've watched it over and over and recommended it to many people. But then again this is just my belief which I'm willing to change in the future based on the data. I believe this makes me biased towards being a Bayesian, but someone correct me if I'm wrong. 😇

I don't know anything about statistics, but it sounds like when each group answers the "what probability is it that it's x?" question, they're focused on two different referents. The frequentists interpret the question as referring to the actual, determinate state of affairs in the world, while the Bayseians interpret it as an epistemological question, that is as a question about our knowledge. Two ways of interpreting what "probability" refers to.

This video was amazing. I find myself with both, but lean toward the Baysian to answer this coin toss question from the perspective of "given the information I have available to me, my answer is ___". But based on this description, frequentist favoring more ground truth, then I would think for something like testing of a medical diagnostic machine accuracy, I would not care about only the information I have, but also the information I don't have because the true answer could be more important.

Cassie, very interesting, which one is best for online A/B testing in your personal opinion?

Is it possible to be a frequentist before the coin is flipped, like the answer of that coin landing heads or tails is already 100% or 0% which is predetermined by a multitude of factors such as its orientation at the moment, how hard you will flip it and so on, all of which are all also pre-determined but we just don’t know them

Other than regularisation, I have yet to find a use for Bayes. The advantage of frequentist is it's really easy to see how it was abused

The way I thought of it was that the chance that an event did/can/will happen is actually always either 100% or 0% and it is just a lack of knowledge that makes it appear otherwise. Or in other words, probability is like a measurement of our own ignorance (are we slightly unsure or very unsure? etc). I don't know if that shit's true, it just looks like it to me.

Quality and practical use go hand in hand.

Thank you for the simple explanation :) As far as I understand, the frequentist statistics is correct. However, from my point of view as a research scientist, the frequentist statistics is often irrelevant! Because I am often interested to know if my model or explanation of a complicated reality is consistent with the observations. These types of questions are consistently addressed within the framework of Bayesian statistics. On the other hand, the Bayesian approach is still missing an important ingredient. Bayesians still do not agree on how to construct priors! How does one construct a prior, which represents one's knowledge?

Finally I get the point of difference between them but I am more confused now which of these I am ? How to deal with that ?

Forgive my stupid question (which might be slightly off-topic), but doesn't it matter which side is facing up before the flip, how the coin is placed on the thumb, how much force it used for the flip, and some other factors (which may or may not be negligible)?

This is a finely done video - props to Kozyrkov for a superb presentation. I think, however, the emphasis on the subjectivity of Bayesian inference is a bit misleading. One comes away with the notion that frequentists are interested in reality while Bayesians are interested in opinions. Surely all practitioners of data-based inference are interested in reality; the difference lies in kinds of questions by which reality is sussed out. The Bayesian and the frequentist might agree that a given state or process in the world can be understood in terms of definite parameters, i.e. that the flipped coin has already landed. To say that the Bayesian approach is subjective is simply to say that it is concerned with *our knowledge* - or, equivalently, our *uncertainty* - regarding the parameters of interest given available evidence (data + priors). I suppose this could be called "subjective" since it depends on the knowledge available to a subject, but it is certainly not subjective in the pejorative sense of "arbitrary." In most cases, at least in my field of ecology, the frequentist is also interested in parameter states. That, after all, is what it means when we ask whether X causes Y. But frequentist methods get there indirectly by inferring the likelihood of evidence (data only, no priors) given assumed parameter states. While these approaches generate parameter estimates (parameter values that maximize the likellihood of the data) with uncertainty (intervals that would contain the true parameter value in X% of hypothetical repetitions of the sampling and analysis process), they do not tell us directly what we really want to know: what should we believe about the unknown state of the paramater? This is what we want to *know* because it guides what we want to *do*, i.e. to understand and potentially intervene in the world. These objectives, like our knowledge, are intrinsically subjective, but in a sense that is both legitimate and unavoidable. I also think it is a mistake - not one made explicitly by Kozyrkov, but one occasionally suggested by others - to project approaches to data-based inference onto metaphysics. Choosing between frequentist and Bayesian methodologies should have nothing to do with whether one is an ontological realist or nominalist. As Andrew Gelman puts it, "theoretical statistics is the theory of applies statistics." Pragmatic handling of uncertainty, appropriate to the question at hand, is the only end for which statistics is a legitimate means.

I kind of understand, a frequentist sounds like they care about what is "possible", if there are two possible options, like heads or tails and an event which has a before and an after. Before the event we can consider those 2 possibilities. After the event we can consider the outcome but there is no possibilities to consider, as one them was realised. If you have been taking prior beliefs and outcomes into account then you would have something to consider.

Thanks.

But when we talk about Bayesians view, then one would need to mention Bayesian networks. And those shall rather be compared with the coin example. Because in Bayesian Nets you would actually construct a graph with a node saying "coin was flipped" and then dealing with the probability of the coin being flipped. That's were also the strengths of a BN approach lie. When you would need to narrow down in a (short) amount of events that certainly influence the outcome. So each approach heavly relies on the hypothesis to test. The more unknown factors you have the more you tend towards a frequentists view. Right?

Mathematically speaking (I am not a Mathematician, just a software developer), bayesians answers the question about the probability of the coin position based on given data, meaning "the coin has been thrown, and landed on either side" (it's important, since it could have landed vertically.. a very slight probability, but not really 0%... but since it has been stated it could only be heads or not, this possibility is discarded) "but since there is no actual data, and there are no more options, the probability is 50% for each one; Bayesian answers the question asked with the given data. Of course, similar to the Schrödinger's cat, there is no *certainty* about the results (although the coin's position IS determined, not a quantum state :-)), the Bayesian gives the most "reliable" answer: "50%". Obviously, if a person answers "0 or 100" it will be correct, but these are TWO answers, both have a 50% probability of being right, which is not what was asked: that the coin can be heads or tails IS THE PREMISE, so I could not use it as an ANSWER.Right...?

How does this apply to quantum superposition?

I'm trying to do Bayesian inference where the prior and likelihood distributions are Cauchy distributions. Can you (or anyone else) point me in the direction of how to do that? There are lots of resources online of how to do Bayesian inference with normal distributions and beta and gamma distributions, but I don't see anything involving Cauchy distributions.

What's the frequentist perspective on getting the model right? It always seemed to be like bayseans try to make that more explicit but I struggle to see a real distinction, but I'm kind of convinced (after adjusting my prior ;-) I just don't understand the semantic distinction that the frequentist perspective had with respect to (implicit) assumptions