ABSTRACT
Bayesian computation revolves around two steps: computation of the posterior distribution, p(θ|y), and computation of the posterior predictive distribution, p(y˜|y). So far we have considered examples where these could be computed analytically in closed form, with simulations performed directly using a combination of preprogrammed routines for standard distributions (normal, gamma, beta, Poisson, and so forth) and numerical computation on grids. For complicated or unusual models or in high dimensions, however, more elaborate algorithms are required to approximate the posterior distribution. Often the most efficient computation can be achieved by combining different algorithms. We discuss these algorithms in Chapters 11-13. This chapter provides a brief summary of statistical procedures to approximately evaluate integrals. The bibliographic note at the end of this chapter suggests other sources.
