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Nowadays there are many papers on the number theory using heuristics.

I have read some of them. But I have no clear understanding of the Bayesian Probability(subjective probability).

The concept of using probabilistic method for a deterministic object is not clear at least to me.

Is there any good exposition on the Bayesian Probability especially for number theorists?

Thank you.

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    $\begingroup$ Possibly relevant paper arxiv.org/abs/1707.08747 . $\endgroup$ Commented Jul 2, 2020 at 14:29
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    $\begingroup$ By the way, it would be interesting to establish some kind of "extremal probability entropy principle", which would allow to determine which probability distribution is best suited to apprehend a deterministic mathematical phenomenon heuristically. $\endgroup$ Commented Jul 2, 2020 at 14:34
  • $\begingroup$ @SylvainJULIEN I agree with that. And I hope those discussions could become easily accessible to number theorists. Is the 'extremal probability entropy principle' a well established concept? If so can you suggest a good reference please? $\endgroup$ Commented Jul 2, 2020 at 14:41
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    $\begingroup$ I don't know actually. I was just trying to draw a parallel with both the maximum entropy principle and the extremal action principle in physics (I studied physics). A fun fact is that these two principles can be expressed as $\delta S=0$ with of course different meanings for the symbol $S$! But the Shannon entropy of a probability distribution is well defined, so you should be able to find relevant references about it. $\endgroup$ Commented Jul 2, 2020 at 14:52

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