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Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator
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Doucet, A., Pitt, Michael K., Deligiannidis, G. and Kohn, R. (2015) Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator. Biometrika, 102 (2). pp. 295-313. doi:10.1093/biomet/asu075 ISSN 0006-3444.
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WRAP-efficient-Markov-chain-unbiased-likelihood-estimator-Pitt-2015.pdf - Accepted Version - Requires a PDF viewer. Download (1429Kb) | Preview |
Official URL: http://dx.doi.org/10.1093/biomet/asu075
Abstract
When an unbiased estimator of the likelihood is used within a Metropolis–Hastings chain, it is necessary to trade off the number of Monte Carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain. Using many Monte Carlo samples will typically result in Metropolis–Hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples; however, the computing time required to construct the likelihood estimator increases with the number of samples. Under the assumption that the distribution of the additive noise introduced by the loglikelihood estimator is Gaussian with variance inversely proportional to the number of samples and independent of the parameter value at which it is evaluated, we provide guidelines on the number of samples to select. We illustrate our results by considering a stochastic volatility model applied to stock index returns.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Social Sciences > Economics | |||||||||
| Library of Congress Subject Headings (LCSH): | Markov processes, Monte Carlo method | |||||||||
| Journal or Publication Title: | Biometrika | |||||||||
| Publisher: | Biometrika Trust | |||||||||
| ISSN: | 0006-3444 | |||||||||
| Official Date: | 1 June 2015 | |||||||||
| Dates: |
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| Volume: | 102 | |||||||||
| Number: | 2 | |||||||||
| Page Range: | pp. 295-313 | |||||||||
| DOI: | 10.1093/biomet/asu075 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 26 July 2018 | |||||||||
| Date of first compliant Open Access: | 26 July 2018 | |||||||||
| RIOXX Funder/Project Grant: |
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