Nonnormal Approximations to Likelihoods and Posteriors

Abstract

In this chapter, we continue our presentation of methods which are applied directly to the likelihood or to the posterior. However, in this chapter we work with higher-order approximations to these functions. In Section 3.1, we discuss numerical integration as a method to obtain a close approximation to the marginal of the posterior or of the likelihood. Section 3.2 approaches the problem of higher-order approximations to the posterior or to the likelihood from the point of view of Laplace’s method. Section 3.3 presents the methods of Monte Carlo, importance sampling and rejection/acceptance to realize a sample from the function of interest. Iterative Monte Carlo methods are presented in chapters 5 and 6.