Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
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
Published inScandinavian Journal of Statistics
© Wiley-Blackwell, 2020
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. ...
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Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF; Research post as Academy Research Fellow, AoF; Research costs of Academy Research Fellow, AoF
Additional information about fundingThe authors have been supported by the Academy of Finland grants 274740, 284513, 312605 and 315619.
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