Parallel Gaussian process surrogate Bayesian inference with noisy likelihood evaluations

Marko Järvenpää, Michael U. Gutmann, Aki Vehtari, Pekka Marttinen

Research output: Contribution to journalArticlepeer-review


We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method is used to form the noisy log-likelihood estimates using computationally costly forward simulations. We frame the inference task as a sequential Bayesian experimental design problem, where the log-likelihood function is modelled with a hierarchical Gaussian process (GP) surrogate model, which is used to efficiently select additional log-likelihood evaluation locations. Motivated by recent progress in the related problem of batch Bayesian optimisation, we develop various batch-sequential design strategies which allow to run some of the potentially costly simulations in parallel. We analyse the properties of the resulting method theoretically and empirically. Experiments with several toy problems and simulation models suggest that our method is robust, highly parallelisable, and sample-efficient.
Original languageEnglish
Pages (from-to)147-178
Number of pages32
JournalBayesian analysis
Issue number1
Early online date19 Mar 2020
Publication statusPublished - 1 Jan 2021


  • expensive likelihoods
  • likelihood-free inference
  • surrogate modelling
  • Gaussian processes
  • sequential experiment design
  • parallel computing


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