Adaptive multiple importance sampling for Gaussian processes. Issue 8 (24th May 2017)

• Record Type: Journal Article
• Authors: Xiong, Xiaoyu; Šmídl, Václav; Filippone, Maurizio
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 8(2017)
• Page Start: 1644
• Page End: 1665
• Publication Date: 2017-05-24
• Subjects: Gaussian processes -- Bayesian inference -- Markov chain Monte Carlo -- importance sampling; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2017.1280037
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: In applications of Gaussian processes (GPs) where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. This is normally done by means of standard Markov chain Monte Carlo (MCMC) algorithms, which require repeated expensive calculations involving the marginal likelihood. Motivated by the desire to avoid the inefficiencies of MCMC algorithms rejecting a considerable amount of expensive proposals, this paper develops an alternative inference framework based on adaptive multiple importance sampling (AMIS). In particular, this paper studies the application of AMIS for GPs in the case of a Gaussian likelihood, and proposes a novel pseudo-marginal-based AMIS algorithm for non-Gaussian likelihoods, where the marginal likelihood is unbiasedly estimated. The results suggest that the proposed framework outperforms MCMC-based inference of covariance parameters in a wide range of scenarios.