Bayesian philosophy of science tells us that what we should believe about a theory in the light of evidence depends on the posterior probability that the theory is true, that is, the probability of theory after we see the evidence. According to Bayes's Rule, this probability is proportional to a prior times a likelihood. A likelihood is the probability of observing some evidence given that a theory is true; a prior is the probability that the theory is true before we see the evidence.
Here anti-Bayesians object: where does this prior probability come from? There's no use saying that it's just the posterior resulting from earlier evidence. That only pushes the problem back one step, threatening an infinite regress.
What about a Principle of Indifference? If we can't say how probable a theory is before we see the evidence, perhaps we can express our ignorance, and say that such-and-such competing theories are all equally likely. Unfortunately, that doesn't work either: it depends on how you describe the theories. You can make the answers come out any way you please.
It seems we need some other basis for our prior probabilities -- but what? Until now, Bayesians have had no answer, and it looked like Bayesianism was sunk. But now a surprising answer has come from a surprising quarter: from computer science and the work of Chris Wallace. Where do prior convictions come from? From Turing Machines!
CSE1370/CSE2370: This is one of a series of occasional talks on varied topics for interested 1st and 2nd year computing students. The talks are associated with CSE1370/CSE2370, a zero-point unit `Advanced First/Second-year Projects'; zero points but it does appear on your academic record. (Note that anyone can attend the talks.) The projects are for interested students and run in 2nd semester. Staff members, and postgraduates, will offer project topics in Computer Science, Software Engineering and related fields. But if you have a particular project idea of your own, contact Lloyd Allison who will try to find a supervisor for it.