Are you Bayesian or Frequentist?

What if I told you I can show you the difference between Bayesian and Frequentist statistics with one single coin toss?

SUMMARY
It is only by insisting that the parameter may not be a random variable (Frequentist) that it makes any kind of sense to talk about your method's ability to deliver the right answer. As soon as you let the parameter be a random variable (Bayesian), there's no longer any notion of right and wrong.   

BAYES VS FREQUENTIST... FIGHT!

What words tell you that we're wading through their territory?
What are they using statistics to change their minds about?
What is the main difference?
What do you win if you choose this side?
What do you lose if you choose this side?
So, which one is better?
Okay... so which one is more objective and "correct"?
What about small vs large sample sizes as a criterion?
Cassie, you're killing us here. Are you Bayesian or Frequentist?
Should I pick a side?

Learn more:

[lrgui]

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.

[soonny]

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?

[solsav]

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.

[juancampos]

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)

[donnachafitzgerald]

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!

[IanALane]

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

[alexeyzelenskiy]

Thank you. Perfect pausing during the presentation. It is so rare among YouTube presenters.

[banana]

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.

[jamescrud]

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.

[marktahu]

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.

[traininggrounds]

Let's not start making a rigorous mathematical discipline into a mystical personality quiz. Bayesian and "Frequentist" thinking are NOT acceptable to be said they are a "way to think" or something to like or have a certain personality about. It's literally in how you phrase the question that determines whether the answer is Bayesian or Frequentist. If you ask, "What is the probability I WILL flip a coin heads?" versus "What is the probability this coin IS heads up right now?" then this is the fundamental difference between the two aforementioned "modes" of an outcome. It has nothing to do with how you feel about but how you phrase the question. It's just two different aspects of probability given that the trial is soon to be finished or already finished.

[MrDemoncrusher]

*Neo* "Heads!"

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

[P_Mann]

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.

[the_trevoir]

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

[LegoEddy]

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 :)

[louisbademosi]

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

[ironnerd]

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.

[phg]

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

[PACXS]

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.

[brunosignoriwustro]

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.