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The Bayesian paradigm provides an elegant framework for resolving problems of uncertainty by permitting one to treat all unknown parameters as random variables and thus impose prior probability distributions over them. This chapter begins by showing how this approach allows one to make explicit statements about the probability distributions of future observations, and then argues in favor of a “fundamentalist” (or “literalist”) Bayesian approach to generating prior probability distributions. Next, it introduces the expected-utility principle in a Bayesian context and explains how it leads to a very natural system for making decisions in the presence of uncertainty. Finally, it shows how the Bayesian decision framework is sufficiently powerful to address problems of extreme (Knightian) uncertainty.
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