Flexible Effective Sample Size Based on the Message Importance Measure

In Monte Carlo based importance sampling estimations, Effective Sample Size (ESS) is an important index of simulation efficiency, since ESS can measure the divergence between the target distribution and the proposal distribution effectively, and thus is widely used to decide whether resampling is needed or not. Among several well-known variants of ESS, the Shannon entropy based perplexity has been widely used. In this paper, however, we propose a new ESS function (E-MIM) by using the message importance measure (MIM) instead of Shannon entropy. We show that E-MIM satisfies all of the five conditions for ESS generalizations. We also propose an MIM based divergence and investigate its approximation to E-MIM. Moreover, we present a resampling threshold selection method for the ratio between E-MIM and the corresponding actual sample size. Finally, we investigate the performance of E-MIM and other ESS functions through numerical simulations. By a particle filter experiment, we show that E-MIM outperforms other ESS functions in terms of mean-squared error.