[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... ).

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... )

[bkcooper]

I understand all of this, and yes, plainly in the case of ESP cheating seems much more likely than genuine ESP. My point is that there's nothing in the overall process to prevent this sort of subversion:

* do an experiment;

* get result that doesn't comport with your beliefs;

* retroactively decide "aha, a hypothesis I hadn't considered!" and assign it a greater prior, thereby making it the thing for which you are actually generating evidence.

What I am trying to argue is that this last step is uncontrolled and highly gameable since there's no limit to the amount of possible hypotheses you could dream up (and thus you could keep fishing until you find one you like.) I don't feel that all of the maxent stuff later in the book does much to help you choose priors for this sort of thing.

[dthunt]

Oh, part of that explanation assumes you know how to use Bayes' Theorem. If you don't, this doesn't look like a simple explanation, it probably looks like the ravings of a madman because I'm assuming you know a few of the properties and common manipulations of the formula.