Rethinking the Effective Sample Size

Victor Elvira, Luca Martino, Christian P. Robert

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The effective sample size (ESS) is widely used in sample-based simulation methods for assessing the quality of a Monte Carlo approximation of a given distribution and of related integrals. In this paper, we revisit the approximation of the ESS in the specific context of importance sampling (IS). The derivation of this approximation, that we will denote as ESSˆ, is partially available in Kong (1992). This approximation has been widely used in the last 25 years due to its simplicity as a practical rule of thumb in a wide variety of importance sampling methods. However, we show that the multiple assumptions and approximations in the derivation of ESSˆ, makes it difficult to be considered even as a reasonable approximation of the ESS. We extend the discussion of the ESSˆ in the multiple importance sampling (MIS) setting, we display numerical examples, and we discuss several avenues for developing alternative metrics. This paper does not cover the use of ESS for MCMC algorithms.
Original languageEnglish
Pages (from-to)525-550
JournalInternational Statistical Review
Volume90
Issue number3
Early online date10 Apr 2022
DOIs
Publication statusPublished - 31 Dec 2022

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