A1 Journal article (refereed)
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo (2020)

Vihola, M., Helske, J., & Franks, J. (2020). Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo. Scandinavian Journal of Statistics, 47(4), 1339-1376. https://doi.org/10.1111/sjos.12492

JYU authors or editors

Vihola, Matti
Helske, Jouni
Franks, Jordan

Publication details

All authors or editors: Vihola, Matti; Helske, Jouni; Franks, Jordan

Journal or series: Scandinavian Journal of Statistics

ISSN: 0303-6898

eISSN: 1467-9469

Publication year: 2020

Publication date: 03/09/2020

Volume: 47

Issue number: 4

Pages range: 1339-1376

Publisher: Wiley-Blackwell

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1111/sjos.12492

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71682

Publication is parallel published: https://arxiv.org/abs/1609.02541

Abstract

We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically operates on the hyperparameters, and the subsequent weighting may be based on IS or sequential Monte Carlo (SMC), but allows for multilevel techniques as well. The IS approach provides a natural alternative to delayed acceptance (DA) pseudo-marginal/particle MCMC, and has many advantages over DA, including a straightforward parallelisation and additional flexibility in MCMC implementation. We detail minimal conditions which ensure strong consistency of the suggested estimators, and provide central limit theorems with expressions for asymptotic variances. We demonstrate how our method can make use of SMC in the state space models context, using Laplace approximations and time-discretised diffusions. Our experimental results are promising and show that the IS type approach can provide substantial gains relative to an analogous DA scheme, and is often competitive even without parallelisation.

Keywords: statistical methods; Bayesian analysis; sampling (statistical methods); estimating (statistical methods); Markov chains; Monte Carlo methods

Free keywords: Markov chain Monte Carlo (MCMC); Bayesian analysis

Fields of science: