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 toimittajatFranks, Jordan; Vihola, Matti

Lehti tai sarjaStochastic Processes and Their Applications

ISSN0304-4149

eISSN1879-209X

Julkaisuvuosi2020

Volyymi130

Lehden numero10

Artikkelin sivunumerot6157-6183

KustantajaElsevier

JulkaisumaaAlankomaat

Julkaisun kielienglanti

DOIhttps://doi.org/10.1016/j.spa.2020.05.006

Julkaisun avoin saatavuusEi avoin

Julkaisukanavan avoin saatavuus

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

Julkaisu on rinnakkaistallennettuhttps://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-asiasanatstokastiset prosessitMarkovin ketjutMonte Carlo -menetelmätestimointinumeeriset menetelmät

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


Liittyvät organisaatiot


Hankkeet, joissa julkaisu on tehty


OKM-raportointiKyllä

Raportointivuosi2020

JUFO-taso2


Viimeisin päivitys 2024-22-04 klo 11:43