A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance (2020)

Franks, J., & Vihola, M. (2020). Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance. Stochastic Processes and Their Applications, 130(10), 6157-6183. https://doi.org/10.1016/j.spa.2020.05.006

JYU-tekijät tai -toimittajat

Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Franks, Jordan; Vihola, Matti

Lehti tai sarja: Stochastic Processes and Their Applications

ISSN: 0304-4149

eISSN: 1879-209X

Julkaisuvuosi: 2020

Volyymi: 130

Lehden numero: 10

Artikkelin sivunumerot: 6157-6183

Kustantaja: Elsevier

Julkaisumaa: Alankomaat

Julkaisun kieli: englanti

DOI: https://doi.org/10.1016/j.spa.2020.05.006

Julkaisun avoin saatavuus: Ei avoin

Julkaisukanavan avoin saatavuus: 

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/69233

Julkaisu on rinnakkaistallennettu: https://arxiv.org/abs/1706.09873

Tiivistelmä

We establish an ordering criterion for the asymptotic variances of two consistent Markov chain Monte Carlo (MCMC) estimators: an importance sampling (IS) estimator, based on an approximate reversible chain and subsequent IS weighting, and a standard MCMC estimator, based on an exact reversible chain. Essentially, we relax the criterion of the Peskun type covariance ordering by considering two different invariant probabilities, and obtain, in place of a strict ordering of asymptotic variances, a bound of the asymptotic variance of IS by that of the direct MCMC. Simple examples show that IS can have arbitrarily better or worse asymptotic variance than Metropolis–Hastings and delayed-acceptance (DA) MCMC. Our ordering implies that IS is guaranteed to be competitive up to a factor depending on the supremum of the (marginal) IS weight. We elaborate upon the criterion in case of unbiased estimators as part of an auxiliary variable framework. We show how the criterion implies asymptotic variance guarantees for IS in terms of pseudo-marginal (PM) and DA corrections, essentially if the ratio of exact and approximate likelihoods is bounded. We also show that convergence of the IS chain can be less affected by unbounded high-variance unbiased estimators than PM and DA chains.

YSO-asiasanat: stokastiset prosessit; Markovin ketjut; Monte Carlo -menetelmät; estimointi; numeeriset menetelmät

Vapaat asiasanat: asymptotic variance; delayed-acceptance; importance sampling; Markov chain Monte Carlo; pseudo-marginal algorithm; unbiased estimator

Liittyvät organisaatiot

Hankkeet, joissa julkaisu on tehty

OKM-raportointi: Kyllä

VIRTA-lähetysvuosi: 2020

JUFO-taso: 2