English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We establish an ordering criterion for the asymptotic variances of twoconsistent Markov chain Monte Carlo (MCMC) estimators: an importance sampling(IS) estimator, based on an approximate reversible chain and subsequent ISweighting, and a standard MCMC estimator, based on an exact reversible chain.Essentially, we relax the criterion of the Peskun type covariance ordering byconsidering two different invariant probabilities, and obtain, in place of astrict ordering of asymptotic variances, a bound of the asymptotic variance ofIS by that of the direct MCMC. Simple examples show that IS can havearbitrarily better or worse asymptotic variance than Metropolis-Hastings anddelayed-acceptance (DA) MCMC. Our ordering implies that IS is guaranteed to becompetitive up to a factor depending on the supremum of the (marginal) ISweight. We elaborate upon the criterion in case of unbiased estimators as partof an auxiliary variable framework. We show how the criterion impliesasymptotic variance guarantees for IS in terms of pseudo-marginal (PM) and DAcorrections, essentially if the ratio of exact and approximate likelihoods isbounded. We also show that convergence of the IS chain can be less affected byunbounded high-variance unbiased estimators than PM and DA chains.

Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance