
Frequentists vs Bayesians - thomaspaine
http://infoproc.blogspot.com/2008/12/frequentists-vs-bayesians.html
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Eliezer
I don't think this article does a very good job of explaining the distinction.

I know what a Bayesian is. I'm not sure that even frequentists know what a
frequentist is.

~~~
lliiffee
Roughly (and inaccurately) speaking, frequentism is about confidence
intervals.

Like, suppose someone hands me a biased coin. A frequentist can flip that coin
10 times, then make a bound on the true bias of the coin that holds with the
promised degree of confidence. (E.g. they can make a bound that will hold on
95% of such experiments.)

Bayesians can't do this. There are lots of other advantages to the Bayesian
approach, but to frequentists, nothing could be worth giving up "coverage"
(confidence intervals obeying their guarantees).

P.S. When looking at those ten coin flips, and trying to estimate the true
bias, the frequentist and bayesian will have the following argument:

Bayesian: The probability that the true bias is b is __some formula___

Frequentist: Are you insane? The true bias of the coin _is what it is_! It's a
number! Just because you don't know what that number is doesn't mean anything
probabilistic is going on.

Bayesian: Well it is extremely useful to be allowed to make such statements.

~~~
kurtosis
this is interesting - couldn't a bayesian get many of the same guarantees by
computing the posterior distribution and choosing a range that contains X% of
the mass?

~~~
lliiffee
In a word, no. The reason is that if the bayesian does a really crappy job of
specifying their prior distribution, the posterior will be completely
inaccurate. On the other hand, if the bayesian does a good job, getting
intervals as you describe will work much better (e.g. be smaller) than
confidence intervals.

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brendano
here's a better though longer frequentist vs bayesian article from brad efron.
[http://www-stat.stanford.edu/~ckirby/brad/papers/2005NEWMode...](http://www-
stat.stanford.edu/~ckirby/brad/papers/2005NEWModernScience.pdf)

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Raphael
Would someone explain this in layman's terms?

~~~
tel
Disclaiming that I'm more of a statistics enthusiast than a real statistician,
here's how I understand the schism.

Bayesian (subjective) and Frequentist (objective) are two schools of thought
about how statistics should operate. One of the best ways to think about the
difference is to call Bayesians pragmatic and Frequentists rigorous.

In that face of trying to quantify something you don't know, Bayesians take
the stance that if you just say _something_ — even if it's incorrect — and
then keep adjusting it as more data comes in then you'll eventually have a
valid statement. The idea is that even if your model is only so correct, at
least you have one. Unfortunately, no one can actually prove that sort of
thing actually works all of the time. It just seems to.

Frequentists faced with this situation instead try to understand the reason
why something is happening and then model it from the beginning. By
considering these rigorous models and testing them against data they
eventually build a resilient model for the unknown which validates. That is,
unless they don't, in which case Frequentists are kind of out of luck.

So when you're talking about statistics, which is all about trying to model
things you don't understand, Bayesians and Frequentists get up in arms all the
time because they each have something to call foolish about one another.

The coolest part is that this sort of schism is being reflected in the world
of physics as well where Frequentists are in the Newtonian/Einsteinian school
but, bit by bit, that worldview is being shaken up by Quantum.

~~~
Eliezer
sorry, lkozma below got this right, you didn't.

Bayesians claim to be more rigorous than frequentists, living or dying by the
theorems of probability theory, rather than using a toolbox of ad-hoc tools.
For example. And quantumness has very little to do with it.

~~~
brent
Arbitrary priors don't imply rigor <ducks>.

:-)

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jerf
Reality is frequentist. You are small, consequently you can't do better than
being a Bayesian. And you'll still be wrong.

Bummer.

~~~
JulianMorrison
If reality is deterministic, it can't possibly be frequentist. If you had
total information you would assign every real event probability 1, or some
reliable 0<p<1 for continuity-of-experience with a self traveling down one of
the branches of an as yet unresolved quantum event.

~~~
jerf
Reality does not appear to be deterministic in any sense of the term.

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JulianMorrison
Please clarify.

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jerf
A vague hand wave in the direction of QM?

I'm not sure how to clarify. The idea that reality is deterministic is so
completely unsupported by evidence, I don't even know where to start. Between
uncertainty principles forbidding you from knowing the precise state of the
universe even in principle and the randomness of the universe's behavior even
in situations you have full knowledge of (which may yet be traced back to
mathematical undecidability, per a recent, interesting paper on arxiv),
determinism is _dead_. If they can track it back to mathematical
undecidability, no conceivable heroic effort can bring it back, either. (I
suspect there's some fruitful work to be done there.)

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JulianMorrison
Quantum physics is usefully sketched out for the layperson here:
<http://www.overcomingbias.com/2008/06/the-quantum-phy.html>

It's deterministic. QM objections are based on bad pop sci.

Undecidability in the context of physics sounds interesting, care to add
detail?

~~~
jerf
That series of posts goes beyond the science. I think his arguments boil down
to him simply being unable to accept nondeterminism, and his argument that
many-worlds is inevitable is simply absurd on the face of it; we could be in a
simulation that is based in a universe without many-worlds and you'd never be
able to tell the difference, so it's hardly obvious that even if we're not in
a simulation that many worlds is inevitable. I also think he falls prey to
Euclidianism, which most people do. In a Minkowskian universe, a lot of QM's
nondeterminism is a lot less magical, even if it's still nondeterministic.

