ABSTRACT
The Bayesian formalism treats parameter distributions as relative plausibility, not as any physical random process. This chapter provides basic skills for working with samples from the posterior distribution. Working with samples transforms a problem in calculus into a problem in data summary, into a frequency format problem. An integral in a typical Bayesian context is just the total probability in some interval. The Bayesian parameter estimate is precisely the entire posterior distribution, which is not a single number, but instead a function that maps each unique parameter value onto a plausibility value. The resulting distribution is for predictions, but it incorporates all of the uncertainty embodied in the posterior distribution for the parameter. Expertise in turn allows for imaginative checks of model performance.
