A very good essay on Bayesian probability theory and its applicability to rationality is "A Technical Explanation of Technical Explanation" at http://yudkowsky.net/bayes/technical.html . The beginning is more mathy than the latter half, which is more interesting, so don't let the math keep you from reading it and getting to the more interesting later parts. There isn't much math, and the math that is there is pretty simple. If you haven't been introduced to Bayesian probability, you need to at least skim through the article entitled "An Intuitive Explanation of Bayesian Reasoning" that is linked to from the above URL.
If you decide that Bayesian rationality is totally awesome, read the book "Probability Theory: The Logic of Science" by E. T. Jaynes, which is specifically about Bayesian probability theory and its applications, derived entirely from a list of simple informal "desiderata" that we would expect from a theory of probability. He shows that Bayesian probability theory is the only way to satisfy these simple logical desiderata, and that Bayesian probability theory is the unique consistent and natural extension of Aristotolean logic (True/False logic) to real values.
Bayesian probability is a good topic to be familiar with as a general conceptual tool for evaluating information; it's not just some obscure theorem used by statisticians.
If you decide that Bayesian rationality is totally awesome, read the book "Probability Theory: The Logic of Science" by E. T. Jaynes, which is specifically about Bayesian probability theory and its applications, derived entirely from a list of simple informal "desiderata" that we would expect from a theory of probability. He shows that Bayesian probability theory is the only way to satisfy these simple logical desiderata, and that Bayesian probability theory is the unique consistent and natural extension of Aristotolean logic (True/False logic) to real values.
Bayesian probability is a good topic to be familiar with as a general conceptual tool for evaluating information; it's not just some obscure theorem used by statisticians.