Adaptive multiple importance sampling for Gaussian processes

Xiaoyu Xiong*, Václav Šmídl, Maurizio Filippone

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1644-1665
Number of pages22
JournalJournal of Statistical Computation and Simulation
Issue number8
StatePublished - May 24 2017


  • Bayesian inference
  • Gaussian processes
  • importance sampling
  • Markov chain Monte Carlo

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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