Higher-order Bayesian Approximations for Pseudo-posterior Distributions. Issue 8 (13th September 2016)

• Record Type: Journal Article
• Authors: Ruli, Erlis; Ventura, Laura
• Is Part Of: Communications in statistics. Volume 45:Issue 8(2016)
• Page Start: 2863
• Page End: 2873
• Publication Date: 2016-09-13
• Subjects: Asymptotic expansions -- Bayesian computation -- HOTA algorithm -- Laplace approximation -- MCMC -- Nuisance parameter -- Pairwise likelihood -- Partial likelihood -- Pseudo-likelihood -- Tail area; Primary 62F15 -- Secondary 62-04; 62E20; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2014.930902
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract : The theory of higher-order asymptotics provides accurate approximations to posterior distributions for a scalar parameter of interest, and to the corresponding tail area, for practical use in Bayesian analysis. The aim of this article is to extend these approximations to pseudo-posterior distributions, e.g., posterior distributions based on a pseudo-likelihood function and a suitable prior, which are proved to be particularly useful when the full likelihood is analytically or computationally infeasible. In particular, from a theoretical point of view, we derive the Laplace approximation for a pseudo-posterior distribution, and for the corresponding tail area, for a scalar parameter of interest, also in the presence of nuisance parameters. From a computational point of view, starting from these higher-order approximations, we discuss the higher-order tail area (HOTA) algorithm useful to approximate marginal posterior distributions, and related quantities. Compared to standard Markov chain Monte Carlo methods, the main advantage of the HOTA algorithm is that it gives independent samples at a negligible computational cost. The relevant computations are illustrated by two examples.