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Consistent estimation of the accuracy of importance sampling using regenerative simulation

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  • Bhattacharya, Sourabh

Abstract

Importance sampling is a common technique traditionally used in cases where interest lies in estimation of characteristics of a density [pi](1), but samples are available from a different distribution [pi](0). It is important, however, to evaluate the accuracy of the estimate obtained using importance sampling. In cases where samples are obtained using Markov chain Monte Carlo methods, there does not seem to exist in the literature any consistent or easily computable estimate of the variance of the importance sampling estimator. In this paper we propose an estimator based on regenerative simulation that is consistent as well as easily computable.

Suggested Citation

  • Bhattacharya, Sourabh, 2008. "Consistent estimation of the accuracy of importance sampling using regenerative simulation," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2522-2527, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2522-2527
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    3. James P. Hobert, 2002. "On the applicability of regenerative simulation in Markov chain Monte Carlo," Biometrika, Biometrika Trust, vol. 89(4), pages 731-743, December.
    4. Peter W. Glynn & Donald L. Iglehart, 1990. "Simulation Output Analysis Using Standardized Time Series," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 1-16, February.
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    Cited by:

    1. Raices Cruz, Ivette & Lindström, Johan & Troffaes, Matthias C.M. & Sahlin, Ullrika, 2022. "Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    2. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.

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