In this paper, we introduce the pseudo-extended MCMC method as a simple approach for improving the mixing of the MCMC sampler for multi-modal posterior distributions.

Update: I have read the author response and am satisfied with the commitment to elaborate on \beta and \pi and to simplify the Stan PE code with a "pseudo-extended" function. This paper presents a new MCMC sampling method called pseudo-extended MCMC that uses an instrumental distribution to projects the data into a higher-dimensional space where the modes are connected, making it easier for the sampler to mix. A default instrumental distribution based on tempering is provided. The method is compared to existing baselines showing efficacy on three benchmark datasets. The paper is well-placed within the existing literature.

Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or importance sampling (IS) Monte Carlo (MC) simulation algorithms all involve computing ratios of probability density functions (pdfs). On the other hand, classifiers discriminate labeled samples produced by a mixture of two distributions and can be used for approximating the ratio of the two corresponding pdfs.This bridge between simulation and classification enables us to propose pdf-free versions of pdf-ratio-based simulation algorithms, where the ratio is replaced by a surrogate function computed via a classifier. From a probabilistic modeling perspective, our procedure involves a structured energy based model which can easily be trained and is compatible with the classical samplers.

Entity resolution (ER) presents unique challenges for evaluation methodology. While crowdsourcing platforms acquire ground truth, sound approaches to sampling must drive labelling efforts. In ER, extreme class imbalance between matching and non-matching records can lead to enormous labelling requirements when seeking statistically consistent estimates for rigorous evaluation. This paper addresses this important challenge with the OASIS algorithm: a sampler and F-measure estimator for ER evaluation. OASIS draws samples from a (biased) instrumental distribution, chosen to ensure estimators with optimal asymptotic variance. As new labels are collected OASIS updates this instrumental distribution via a Bayesian latent variable model of the annotator oracle, to quickly focus on unlabelled items providing more information. We prove that resulting estimates of F-measure, precision, recall converge to the true population values. Thorough comparisons of sampling methods on a variety of ER datasets demonstrate significant labelling reductions of up to 83% without loss to estimate accuracy.