

Unusual applications of Bayesian reasoning [pdf] - gwern
http://omega.albany.edu:8008/ETJ-PDF/cc5d.pdf

======
thetwiceler
ET Jaynes is the best! Read the whole book!

[http://bayes.wustl.edu/etj/prob/book.pdf](http://bayes.wustl.edu/etj/prob/book.pdf)

~~~
bkcooper
It's certainly worth looking at. I personally find Jaynes's acerbic commentary
entertaining, although I imagine it grates for many. His overall view of
probability is satisfyingly coherent, but I do not consider myself
sufficiently expert to assess whether it is meaningfully better than the
alternatives. And there are places where I believe he is just wrong, e.g. he
seems to reject Bell's inequality and view quantum probability as just another
case of limited information.

There are also times, like in the chapter linked in the parent, where his zeal
is bothersome. He begins the discussion of ESP by saying it would be too
dogmatic to assign a probability of 0 to ESP. But, when faced with the
evidence, he just throws in a bunch of other possible hypotheses that can
explain it:

 _Therefore, this kind of experiment can never convince me of the reality of
Mrs. Stewart’s ESP; not because I assert Pf = 0 dogmatically at the start, but
because the veriﬁable facts can be accounted for by many alternative
hypotheses, every one of which I consider inherently more plausible than Hf,
and none of which is ruled out by the information available to me._

Of course the choice of priors for those other hypotheses were subjective, and
there's no limit on how many other hypotheses one might add to explain away
unpleasant data. This strikes me as more rationalizing than rationalist.

~~~
dthunt
Really? Do you actually think that Jaynes is being unreasonable when he
assigns ESP a prior that is lower than "has some sort of trick" or some other
thing that generally turns out to be the explanatory factor for a magician?

He's saying that ESP is an unlikely explanation. He's saying that it is
Probably Something Else. The experimental data cannot distinguish them. That's
why it's not compelling. It has very little to do with rationalization. It's a
terrible test.

~~~
bkcooper
No, clearly the underlying mechanism that he describes is good. However, as he
admits in the passage I quote, he is so unconvinced by the possibility of ESP
that no tests of this sort could ever convince him. The issue isn't just that
naive tests of ESP are easily cheated, either, because you can apply the same
logic to more stringently controlled tests.

It just seems more honest to me to admit up front in this situation that you
cannot be convinced of ESP (give it prior probability of 0) instead of playing
these games to essentially shift the "dogmatism" onto the choice of
alternative hypotheses and their prior probabilities (which seem chosen to
enforce a posterior probability of ESP of ~0.)

~~~
dthunt
Look. I'll explain it really simple. He's saying it has to be > 0, because he
is unwilling to rule out ESP as a logical possibility. If he assigned it 0, no
matter how good the experimental design was, and no matter what the test was,
he would be unmovable from this position. 0 is forbidden if you want to accept
it as a possibility. This is why he says this. He also is being honest about
his appraisal of the general likelihood of ESP. It's very low. He doesn't
bother to explain how low because it turns out it's IRRELEVANT.

You literally have to believe ESP is the most likely explanation among all the
usual alternatives ALREADY in order to think it was ESP after ingesting the
data, because the data in this test is not EVIDENCE for ESP, because P(E|sort
of works ESP) and P(E|one of the assistants wore glasses and Stewart could see
some reflections) or whatever your remotely plausible alternative - all look
pretty identical.

It is not evidence, in the sense that you cannot do 500, 37,100, or a 1
million card guessing attempts in this setup with this level of detail and
expect it to shift belief of a rational agent. The ratio between the priors of
the usual suspects is going to look the same as your ratio of posteriors
between all the hypotheses after the test.

In order to convince someone of ESP rationally, you need to demonstrate that
it is extremely difficult to cheat under the test conditions, in the sense
that P(E|trickery) goes down.

Your alternative theory ISN'T the null hypothesis. It's a garden variety non-
magical trickster, which exist in great numbers, whereas nobody has yet seen
even a single instance of ESP as it is normally meant.

~~~
gwern
> It is not evidence, in the sense that you cannot do 500, 37,100, or a 1
> million card guessing attempts in this setup with this level of detail and
> expect it to shift belief of a rational agent. The ratio between the priors
> of the usual suspects is going to look the same as your ratio of posteriors
> between all the hypotheses after the test.

Exactly. When you suspect that the evidence is biased (or in other words,
generated by a process _other_ than genuine new physics or supernatural
activity), more iterations of the process cannot give you much more evidence.
What more iterations does is reduce _sampling error_ from random variation,
but it does nothing about _systematic error_. The idea that you can run a
biased experiment 1000 times and get a much more accurate answer than if you
ran it 10 times is an example of what Jaynes calls 'the Emperor of China'
fallacy, which he discusses in another chapter (I excerpt it in
[http://www.gwern.net/DNB%20FAQ#flaws-in-mainstream-
science-a...](http://www.gwern.net/DNB%20FAQ#flaws-in-mainstream-science-and-
psychology) ).

That this is so surprising and novel is an interesting example of a general
problem with null-hypothesis testing: when a significance test 'rejects the
null', the temptation is to take it as confirming the alternative hypothesis.
But this is a fallacy - when you reject the null, you just reject the null.
There's an entire universe of other alternative hypotheses which may fit
better or worse than the null, of which your favored theory is but one
vanishingly small member.

What is necessary to show ESP specifically is to take all the criticisms and
alternatives, and run different experiments which will have different results
based on whether the alternative or ESP is true. (The real problem comes when
it looks like the best experiments showing ESP are at least as rigorous as
regular science and it's starting to become difficult to think of what exactly
could be driving the positive results besides something like ESP:
[http://slatestarcodex.com/2014/04/28/the-control-group-is-
ou...](http://slatestarcodex.com/2014/04/28/the-control-group-is-out-of-
control/) )

------
mdpopescu
That chapter was very interesting... until I got to this:

"Scientists can reach agreement quickly because we trust our experimental
colleagues to have high standards of intellectual honesty and sharp perception
to detect possible sources of error. And this belief is justiﬁed because,
after all, hundreds of new experiments are reported every month, but only
about once in a decade is an experiment reported that turns out later to have
been wrong."

Er.. what?

[http://www.plosmedicine.org/article/info%3Adoi%2F10.1371%2Fj...](http://www.plosmedicine.org/article/info%3Adoi%2F10.1371%2Fjournal.pmed.0020124)

"Why Most Published Research Findings Are False"

(Ok, so Ioannidis' article was written a year later than the book, but that's
a pretty nasty blow to the argument.)

~~~
mdpopescu
A second problem...

"As a simple, but numerically stronger example illustrating this, if we toss a
coin 1000 times, then no matter what the result is, the speciﬁc observed
sequence of heads and tails has a probability of only 2^−1000"

No... if you toss a coin a thousand times, the probability of observing the
exact sequence you just observed is 1. It will ALWAYS happen (that's what
probability 1 means). Yes, if you had an independent specification for the
sequence (like writing it down before tossing the coin, or converting the
binary representation to ASCII and discovering it spells "Kilroy was here")
then the probability would indeed be 2^-1000; but that would be a different
case.

~~~
dthunt
It's actually not a problem. You can come up with any number of hypotheses
about coins. Some of them take the form, "This coin will produce <some
specific output> in the next 1000 typical flips". That hypothesis and others
with similar, more complex form, like the pair of hypotheses that predict flip
1001 after the same first 1000, GAIN CREDENCE when you perform 1000 flips that
conform to them. Others of the similar form lose it. Other hypotheses of
wildly different construction, like, that a coin is more or less fair, lose
and gain credence according to whether or not they predict the observed
result.

The fact that you didn't write a hypothesis down before you did the test has
very little to do with whether or not the data supports the hypothesis.
Hindsight bias matters, but only as far as it corrupts your experience. The
machine with the infinite library of coin-flip-hypotheses updates just fine.

On a side note, coins are not fair, in general, and Jaynes actually goes into
some detail about the process of cheating at coin flips.

------
beefman
"Unusual", really?

~~~
loup-vaillant
Unusual at the time. It surprised me, but I was reading LessWrong for 2 years
before I read this, and have internalized the notion that probability theory
is basically universally applicable.

But back then when Frequentism dominated, I believe we tended to limit
probability theory to reproducible experiments.

