There are 10 different urns, each with 10 balls.

Urn contains black balls and white balls. What is the probability that we have urn? The conditional probability of drawing balls from urn is :. The joint probability contains all the information we need. We simply consider the subspace highlighted in the figure above and properly normalize it. The normalization factor is :.

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Once you learn the jargon, reading stats articles becomes a lot easier! People can get rather semantic here. The likelihood function is not a probability distribution. In many cases, our prior knowledge is zero, so we give each possibility an equal probability. It all gets a bit messy, judgement enters, and … oh no!

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## Bayesian reasoning in high-energy physics: Principles and applications - INSPIRE-HEP

What happened to scientific objectivity? Setting aside the rigour of the evidence for instance, how sure am I my stone is really blue and came from that bag? We have well-established theories which have passed many tests, so a result claiming new physics amounts to an extraordinary claim, demanding extraordinary evidence.

It is also what humans do in general, and the mathematical tools of probability simply allow us to acknowledge that, and to make the exercise explicitly reproducible, which is surely a good scientific attribute. For example, as a writer and head of a physics department, I get quite a few unsolicited communications about new theories of physics, often involving Einstein having been wrong, or the Higgs boson actually being a macaroon or something.

I have a prior bias here, based on the enormous amount of existing evidence. Einstein might have been confused about the cosmological constant on occasion, but given prior evidence it is highly unlikely that the whole thrust of relativistic mechanics is up the spout. Likewise, I personally have quite a lot of evidence that the Higgs boson is consistent so far with being the fundamental Higgs of the Standard Model, and inconsistent with the macaroon theory. And the others. Jim Al-Khalili was being Bayesian when he promised to eat his boxer shorts if neutrinos travelled faster-than-light.

He was correct. Climate change is another good example.

If you have a prior assumption that modern life is rubbish and technology is intrinsically evil, then you will place a high prior probability on carbon dioxide emissions dooming us all. On the other hand, if your prior bias is toward the idea that there is a massive plot by huge multinational environmental corporations, academics and hippies to deprive you of the right to drive the kids to school in a humvee, you will place a much lower weight on mounting evidence of anthropogenic climate change. If your prior was roughly neutral, you will by now be pretty convinced that we have a problem with global warming.

In any case, anyone paying attention as evidence mounts would eventually converge on the right answer, whatever their prior — though it may come too late to affect the outcome, of course. A prior assumption of zero probability can never be changed. Thus, for example, if you absolutely believe that the Earth is 5, years old or so, no amount of evidence can change your mind. If your unshakeable faith tells you there are only red stones, then the fact that I appear to have a blue one is simply god, or possibly satan, making a red stone look blue to test your faith. By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service.

## Belief, bias and Bayes

Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. In quantum mechanics, we deal with probability. There are two kinds of interpretations: frequency and Bayesian.

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Which one is actually used in quantum mechanics? My impression is, it doesn't matter. However, I would like to know if my understanding is correct.

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I am not sure if this is opinion-based question. According to Jaynes , the different interpretations of probability do matter in QM. Not in terms of experimental outcomes, as the formalism gives the same predictions regardless of interpretation, but on how to interpret some "paradoxical" situations.

But the interesting point made by Jaynes is that Bell , because the way he interprets probabilities, made a mistake in his inequalities' theorem when he wrote the conditional probabilities. The right way to do it, according to Jaynes, is using bayesian rules, which results in a slightly different form for the equations that Bell's uses see p.

The result, according to Jaynes, is that Bell, left out an entire class of hidden variable theories because of its restricted point of view. I am not aware if Jaynes arguments have been debunked, though. But in regard to the problem of overcoming the interpretational problems of the quantum mechanics of pure states, Jaynes did not make much progress.

And I think the reason for this lay partly in the form of the rational Bayesian probability theory he championed.

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This was essentially the logical theory of probability in which probability of a proposition is plausibility of that particular proposition given the truth of certain other propositions. Although he referred to these other propositions as representing actual or supposed knowledge of the reasoner , Jaynes did not give much consideration to the fact that acquisition of that knowledge might affect the probability of the particular proposition on account of the uncertainty principle. Since we expect this to be so, we should, I think, switch to a more subjective approach to probability - to a Bayesian approach that sees the probability of a proposition as our degree of belief in the truth of that proposition given our knowledge.

This is different whenever the uncertainty principle is active i. We should therefore no longer refer to probabilities on condition certain propositions are true, but on condition we know them to be true.