Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
本文提出一种基于近似边际MCMC的重要性抽样加权估计量，适用于贝叶斯潜变量模型，相比延迟接受法更易并行化且灵活，实验显示其性能优越。
Abstract 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 MCMC typically operates on the hyperparameters, and the subsequent weighting may be based on IS or sequential Monte Carlo (SMC), but allows for multilevel techniques as well. The IS approach provides a natural alternative to delayed acceptance (DA) pseudo‐marginal/particle MCMC, and has many advantages over DA, including a straightforward parallelization and additional flexibility in MCMC implementation. We detail minimal conditions which ensure strong consistency of the suggested estimators, and provide central limit theorems with expressions for asymptotic variances. We demonstrate how our method can make use of SMC in the state space models context, using Laplace approximations and time‐discretized diffusions. Our experimental results are promising and show that the IS‐type approach can provide substantial gains relative to an analogous DA scheme, and is often competitive even without parallelization.