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
