Truncated importance sampling

Research output: Contribution to journalArticle

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Abstract

Importance sampling is a fundamental Monte Carlo technique. It involves generating a sample from a proposal distribution in order to estimate some property of a target distribution. Importance sampling can be highly sensitive to the choice of proposal distribution, and fails if the proposal distribution does not sufficiently well approximate the target. Procedures that involve truncation of large importance sampling weights are shown theoretically to improve on standard importance sampling by being less sensitive to the proposal distribution and having lower mean squared estimation error. Consistency is shown under weak conditions, and optimal truncation rates found under more specific conditions. Truncation at rate n1/2 is shown to be a good general choice. An adaptive truncation threshold, based on minimizing an unbiased risk estimate, is also presented. As an example, truncation is found to be effective for calculating the likelihood of partially observed multivariate diffusions. It is demonstrated as a component of a sequential importance sampling scheme for a continuous time population disease model. Truncation is most valuable for computationally intensive, multidimensional situations in which finding a proposal distribution that is everywhere a good approximation to the target distribution is challenging.

LanguageEnglish (US)
Pages295-311
Number of pages17
JournalJournal of Computational and Graphical Statistics
Volume17
Issue number2
DOIs
StatePublished - Jun 1 2008

Fingerprint

Importance Sampling
Truncation
Target
Sequential Importance Sampling
Monte Carlo Techniques
Estimation Error
Importance sampling
Mean Squared Error
Estimate
Continuous Time
Likelihood
Approximation

Keywords

  • Diffusion
  • Monte Carlo
  • Sequential Monte Carlo

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics

Cite this

Truncated importance sampling. / Ionides, Edward L.

In: Journal of Computational and Graphical Statistics, Vol. 17, No. 2, 01.06.2008, p. 295-311.

Research output: Contribution to journalArticle

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