A randomized multi-index sequential Monte Carlo method

Abstract We consider the problem of estimating expectations with respect to a target distribution an unknown normalizing constant, and where even unnormalized needs be approximated at finite resolution. Under such assumption, this work builds upon recently introduced multi-index sequential Monte Carlo (SMC) ratio estimator, which provably enjoys complexity improvements (MIMC) efficiency SMC for inference. The present leverages randomization strategy remove bias entirely, simplifies estimation substantially, particularly in MIMC context, choice index set is otherwise important. reasonable assumptions, proposed method achieves same canonical MSE $$^{-1}$$ - 1 as original (where mean squared error), but without discretization bias. It illustrated on examples Bayesian inverse spatial statistics problems.