Sequentially Guided MCMC Proposals for Synthetic Likelihoods and Correlated Synthetic Likelihoods
Journal article, 2022

Synthetic likelihood (SL) is a strategy for parameter inference when the likelihood function is analytically or computationally intractable. In SL, the likelihood function of the data is replaced by a multivariate Gaussian density over summary statistics of the data. SL requires simulation of many replicate datasets at every parameter value considered by a sampling algorithm, such as Markov chain Monte Carlo (MCMC), making the method computationally-intensive. We propose two strategies to alleviate the computational burden. First, we introduce an algorithm producing a proposal distribution that is sequentially tuned and made conditional to data, thus it rapidly guides the proposed parameters towards high posterior density regions. In our experiments, a small number of iterations of our algorithm is enough to rapidly locate high density regions, which we use to initialize one or several chains that make use of off-the-shelf adaptive MCMC methods. Our "guided" approach can also be potentially used with MCMC samplers for approximate Bayesian computation (ABC). Second, we exploit strategies borrowed from the correlated pseudo-marginal MCMC literature, to improve the chains mixing in a SL framework. Moreover, our methods enable inference for challenging case studies, when the posterior is multimodal and when the chain is initialised in low posterior probability regions of the parameter space, where standard samplers failed. To illustrate the advantages stemming from our framework we consider five benchmark examples, including estimation of parameters for a cosmological model and a stochastic model with highly non-Gaussian summary statistics.

intractable likelihoods

likelihood-free

Bayesian inference

cosmological parameters

Author

Umberto Picchini

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Umberto Simola

University of Helsinki

Jukka Corander

University of Oslo

Bayesian Analysis

1936-0975 (ISSN) 1931-6690 (eISSN)

Deep learning and likelihood-free Bayesian inference for stochastic modelling

Swedish Research Council (VR) (2019-03924), 2020-01-01 -- 2023-12-31.

Chalmers AI Research Centre (CHAIR), 2020-01-01 -- 2024-12-31.

Subject Categories

Probability Theory and Statistics

DOI

10.1214/22-BA1305

More information

Latest update

2/16/2022