Immortality + Bayesian Statistics can't be two lines that diverge that often.
Indeed, as I reported in Jabba's Shroud of Turin thread, it is quite common for fringe theories to adopt a Bayesian approach, among the proponents who are aware of it. jt512 isn't wrong. You can certainly use purely subjective beliefs -- quantified as probabilities -- for elements of the model. The ability to resolve uncertainty in a model with something other than a random variable is, in many cases, a very powerful thing. But it has to be emphasized (and in textbooks ubiquitously is) that the more informed your beliefs are, the better time you're going to have with Bayes. That's the part Jabba and other fringe theorists skip over. They jump straight to the words "reason reliably using only beliefs." And they ignore entirely the notion that a model which produces only probabilities can never establish an allegation of fact, even when it's printed in bold red letters.
As I many have mentioned, a few years ago I engineeringly helped out a friend who owns our local ISP Here's an example from a tool they use.
Bloomberg tells me that 86% of all email is spam. Thus when an email arrives for a customer, we say there's a prior probability of 0.86 that it is spam. That's a belief, in the Bayesian sense. Although it is a belief informed by historical trends, it is a probability assigned based solely on the fact that the message is a message and therefore "most likely" spam.
Naturally there are many tests they can perform. Two dozen or so, last time they showed me the rule set. One of them is an originator location test. Ten percent of all spam comes from Vietnam, so if the originator is in Vietnam, you say there's a probability 0.10 that it's spam. But that, as well as any other test, is not perfectly accurate. We establish a belief in the rate of false positives (from Vietnam but not spam) and false negatives (not from Vietnam, but still spam) and use those to adjust our belief (the message is spam) based on that new event -- the Vietnam-location test. How is that belief established? In this case, by noting when someone drags a message back into his inbox out of his spam folder. The tool considers that a false positive and updates the "beliefs" associated with the accuracy of each test.
The Vietnam test has a very high false negative rate (not from Vietnam yet still spam) and a relatively low false positive rate (from Vietnam and not spam). You can use any method to establish those beliefs in the false positive and negative rates, but if you just pull numbers out of your kiester then you will get results that reflect those arbitrary beliefs. Where Bayes shines is in its ability to take both failure rates into account. The U.S. sends more spam than Vietnam, p = 0.12. But it sends more legitimate email too. So the false positive and negative rates for the U.S. mitigate the raw probability via Bayes in different ways, producing different numerical results. Each origin country is a separate Bayesian event. In Bayesian terms these are still accounted as "beliefs," since identification of origin by political divisions is somewhat arbitrary. It encodes the belief that the geographical origin of a message relates to its likelihood of being spam.
What emerges from the iteration of Bayes theorem is the posterior probability that an email is spam, which adjusts our prior probability based solely on historical spam rates using information particular to that message -- again incorporating our beliefs about how reliably that information relates to the prior.
Repeat for the rest of the tests.
What comes out the end is the ultimate posterior probability of a message being spam. It's still just a probability. The determination of spamminess as a fact is ultimately the customer's choice. If he drags a message back into his inbox, that's an assertion of the fact "No, this is not spam" even if the ultimately computed posterior probability of its being spam is 0.999. That is the qualitative difference between a Bayesian determination and a finding of fact. At every step of the process we deal in quantified beliefs, not facts. We do a very good job of making those beliefs as predicated as possible upon fact.
Several months ago I listed the example of a Bayesian search to locate one's friend in a casino. In similar fashion, the probability we compute that he will be at some particular gambling station is qualitatively detached from the fact of actually finding him at a particular place.
