MCMC‐driven importance samplers

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on class Layered Adaptive Importance Sampling (LAIS) scheme, which is a family adaptive importance samplers where Markov chain algorithms employed to drive an underlying multiple scheme. The modular nature LAIS allows different possible implementations, yielding variety performance and computational costs. propose enhancements classical setting order increase efficiency reduce cost, both upper lower layers. variants address challenges arising real-world applications, instance with highly concentrated distributions. Furthermore, introduce strategies designing cheaper schemes, instance, recycling samples generated layer using them final estimators layer. Different numerical experiments, considering several challenging scenarios, show benefits proposed schemes comparing benchmark presented literature.