TY - JOUR
T1 - A randomized multi-index sequential Monte Carlo method
AU - Liang, Xinzhu
AU - Yang, Shangda
AU - Cotter, Simon
AU - Law, Kody
PY - 2023/7/4
Y1 - 2023/7/4
N2 - We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption, this work builds upon a recently introduced multi-index Sequential Monte Carlo (SMC) ratio estimator, which provably enjoys the complexity improvements of multi-index Monte Carlo (MIMC) and the efficiency of SMC for inference. The present work leverages a randomization strategy to remove bias entirely, which simplifies estimation substantially, particularly in the MIMC context, where the choice of index set is otherwise important. Under reasonable assumptions, the proposed method provably achieves the same canonical complexity of MSE−1 as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems.
AB - We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption, this work builds upon a recently introduced multi-index Sequential Monte Carlo (SMC) ratio estimator, which provably enjoys the complexity improvements of multi-index Monte Carlo (MIMC) and the efficiency of SMC for inference. The present work leverages a randomization strategy to remove bias entirely, which simplifies estimation substantially, particularly in the MIMC context, where the choice of index set is otherwise important. Under reasonable assumptions, the proposed method provably achieves the same canonical complexity of MSE−1 as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems.
KW - Bayesian Inverse Problems
KW - Sequential Monte Carlo
KW - Multi-Index Monte Carlo
U2 - 10.1007/s11222-023-10249-9
DO - 10.1007/s11222-023-10249-9
M3 - Article
SN - 0960-3174
JO - Statistics and Computing
JF - Statistics and Computing
ER -