Hi friends!
I'm Cassie Kozyrkov, a recovering statistician
and today i'm going to help you understand the philosophical divide
between Bayesian statistics and Frequentist statistics... and in fact this is
going to be a medical diagnostic test to tell you which one
you are you ready? okay! i've got a US
quarter here, nothing special, no shenanigans. it has a heads (that's the
one with the head) and a tails and i'm going to flip this
coin. i'm going to flip this coin until it lands heads or tails
in my hand. so, if it lands on its side or it falls on the floor i'm going to redo
this thing so before i begin what is the
probability that this coin will land heads up on my palm?
and let's round that to one decimal place so that you don't get smart
i hope you're saying 50% or a half i agree with you 50%
okay now i'm gonna flip it next question for you: what is the
probability that this coin is heads up on my palm? what's that you're saying? what's the probability? what's the probability that this coin is heads up? hmm you might be saying one of two things now some of you might be saying for you, Cassie, it's whatever it is for you and for us it's 50%! those of you who like that answer you
have aligned yourself with the Bayesian perspective others of you might be saying the coin, Cassie, is up heads
or tails already... there is no probability about it! that thing has landed.
and so it's a stupid question, actually if it is up heads, the answer is 100% and
if it is up tails, the answer is 0% i don't know which one it is but still, there is an actual correct answer and there is no probability about it that is the Frequentist perspective.
now i want to say about Bayesians they're not insane. they're not, like, "oh it's in some indeterminate state" it's not Schrödinger's coin here they understand that the coin has landed. they understand that just like the Frequentist has understood it they're just not interested in that they are interested in their own
perspective from their point of view in their opinion it is 50% the Frequentist, on the other hand, cares
very much about the true answer the truth has already
been fixed in the universe and if the truth is heads it's 100% the
truth is tails it's 0% and their analysis
is oriented on that truth not on their evolving opinion now when i show you how the coin has landed and in this case i don't know if
you can see it but in this case it is tails up now i ask
you again what's the probability that this coin is up heads
and the answer should be from both the Frequentist and the Bayesian:
0% the difference is when the coin has landed but you haven't
seen the answer the Bayesian will say "from my
perspective, 50%" the Frequentist will say
"the actual answer is 0% or 100% (there's no probability!) i just don't know the answer" now which one should you go with? which philosophical perspective makes sense? they're both terrible in their own ways and they're both beautiful in their own ways see... a Bayesian can never be wrong because it's always their opinion they take a starting opinion they see some evidence they get a new opinion
that's still their opinion doesn't matter if that opinion has
nothing to do with everyone else's opinion
it's just a sensible way of updating your opinion with data
but is there a good standard for how you might collaborate between opinions? meh. it's all about you and it's all about your own perspective and there is no
notion of what are the chances that my method
gives me the wrong answer there is no wrong answer Frequentists, on the other hand, want to say "if i were to repeat this procedure many
many many many times some of those times i would guess correctly some of those times i wouldn't if i guessed heads, i would get it right
50% of the time ...if i did it FREQUENT-ly many
times" (hence the name) they have a notion of *getting it right*
they have a notion of *can i guess the truth properly?*
Bayesians don't have that notion i had an opinion ¯\_(ツ)_/¯ i updated it reasonably with data and i've got a new opinion ¯\_(ツ)_/¯ if that's what you want, Bayesian stats is for you if on the other hand you want to
talk about what are the chances that my method hits
the right answer if i do this method over and over if you want this idea of *the method's quality* i'm doing my analysis at a particular
quality level as captured by power and significance (if you know those
Frequentist things) then the Frequentest method is for you the way i like to think about whether to go Bayesian or to go Frequentist
is statistics is the discipline of changing your mind under uncertainty what would you like to change your mind about? would you like to take
your personal opinion, add data to it, and then see how your opinion should
reasonably change? well then, you want to go Bayesian if you're thinking about it in terms of here is an
action that i'm happy to take by default under ignorance i've got no beliefs but,
you know, i've got a favorite action then does my evidence
change my mind about that action? is the evidence strong enough to
convince me not to take this action or should i just go ahead with the
action? if you're framing things that way then you want to be in a Frequentist
perspective because there you can think about what
is the method's quality with respect to making you
stupidly leave your default action what is the methods quality with respect
to your not leaving your action when you should depending on what kind of reasoning you're here for you might want to go
Bayesian or you might want to go Frequentist
Damn I wish she taught my applied Bayesian and classical inference class in college lol
I'm a statistics-is-witchcraftian and would now like to submit my application for a cauldron permit.