Alternative effective sample size measures for importance sampling

L. Martino, V. Elvira, F. Louzada

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The Effective Sample Size (ESS) is an important measure of efficiency in the Importance Sampling (IS) technique. A well-known approximation of the theoretical ESS definition, involving the inverse of the sum of the squares of the normalized importance weights, is widely applied in literature. This expression has become an essential piece within Sequential Monte Carlo (SMC) methods, using adaptive resampling procedures. In this work, first we show that this ESS approximation is related to the Euclidean distance between the probability mass function (pmf) described by the normalized weights and the uniform pmf. Then, we derive other possible ESS functions based on different discrepancy measures. In our study, we also include another ESS measure called perplexity, already proposed in literature, that is based on the discrete entropy of the normalized weights. We compare all of them by means of numerical simulations.

Original languageEnglish
Title of host publication2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016
PublisherIEEE Computer Society
ISBN (Electronic)978-1-4673-7803-1
ISBN (Print)978-1-4673-7804-8
Publication statusPublished - 24 Aug 2016
Event19th IEEE Statistical Signal Processing Workshop, SSP 2016 - Palma de Mallorca, Spain
Duration: 25 Jun 201629 Jun 2016


Conference19th IEEE Statistical Signal Processing Workshop, SSP 2016
CityPalma de Mallorca


  • Effective Sample Size
  • Importance Sampling
  • Perplexity measure
  • Resampling
  • Sequential Monte Carlo


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