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