Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance
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
Julkaistu sarjassa
Stochastic Processes and Their ApplicationsPäivämäärä
2020Tekijänoikeudet
© 2020 Elsevier BV
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.
...
Julkaisija
ElsevierISSN Hae Julkaisufoorumista
0304-4149Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/35699370
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen AkatemiaRahoitusohjelmat(t)
Akatemiatutkija, SA; Akatemiatutkijan tutkimuskulut, SALisätietoja rahoituksesta
Support has been provided for JF and MV from the Academy of Finland (grants 274740, 284513 and 312605), and for JF from The Alan Turing Institute. JF thanks the organisers of the 2017 SMC course and workshop in Uppsala.Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
Vihola, Matti; Helske, Jouni; Franks, Jordan (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 ... -
Statistical analysis of life sequence data
Helske, Satu (University of Jyväskylä, 2016) -
On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction
Vihola, Matti; Franks, Jordan (Oxford University Press, 2020)Approximate Bayesian computation enables inference for complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation ... -
On resampling schemes for particle filters with weakly informative observations
Chopin, Nicolas; Singh, Sumeetpal S.; Soto, Tomás; Vihola, Matti (Institute of Mathematical Statistics, 2022)We consider particle filters with weakly informative observations (or ‘potentials’) relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of ... -
On the convergence of unconstrained adaptive Markov chain Monte Carlo algorithms
Vihola, Matti (University of Jyväskylä, 2010)
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.