In statistical theory, Bayesians believe that Bayes's theorem is fundamental to the assignment of probabilities to hypotheses, and to the rational process of updating credence, or degree of belief in a hypothesis, as new evidence comes in. Non-Bayesians believe its application is extremely limited, often citing the abstract and artificial nature of the prior probabilities that are required. Non-Bayesians usually believe that the process of statistical testing can produce the rational rejection and acceptance of hypotheses of statistical significance with no involvement of prior attitudes. See also personalism.
http://yudkowsky.net/bayes/bayes.html An introduction to Bayesianism and its applications, with a bibliography
http://www.dmoz.org/Science/Math/Statistics/Bayesian_Analysis/ A list of internet resources on Bayesian statistics