Bayesian Estimation

Abstract

The main goal of Bayesian inference is to derive (from data) a posterior distribution over the latent variables in the model, most notably the parameters of the model. This posterior can be subsequendy used to probabilistically infer the range of parameters (through Bayesian interval estimates, in which we make predictive statements such as “the parameter θ is in the interval [0.5, 0.56] with probability 0.95”), compute the parameters’ mean or mode, or compute other expectations over quantities of interest. All of these are ways to summarize the posterior, instead of retaining the posterior in its fullest form as a distribution, as described in the previous two chapters.