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Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator
- Source :
- Doucet, A, Pitt, M, Deligiannidis, G & Kohn, R 2015, ' Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator ', BIOMETRIKA, vol. 102, no. 2, pp. 295-313 . https://doi.org/10.1093/biomet/asu075
- Publication Year :
- 2015
- Publisher :
- Biometrika Trust, 2015.
-
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 averages computed under this chain. Many Monte Carlo samples will typically result in Metropolis--Hastings averages with lower asymptotic variances than the corresponding Metropolis--Hastings averages using fewer samples. However, the computing time required to construct the likelihood estimator increases with the number of Monte Carlo samples. Under the assumption that the distribution of the additive noise introduced by the log-likelihood estimator is Gaussian with variance inversely proportional to the number of Monte Carlo samples and independent of the parameter value at which it is evaluated, we provide guidelines on the number of samples to select. We demonstrate our results by considering a stochastic volatility model applied to stock index returns.<br />34 pages, 9 figures, 3 tables
- Subjects :
- FOS: Computer and information sciences
Statistics and Probability
General Mathematics
Metropolis-Hastings algorithm
Intractable likelihood
Methodology (stat.ME)
Hybrid Monte Carlo
symbols.namesake
Minimum-variance unbiased estimator
Bias of an estimator
Particle filter
Statistics
Stein's unbiased risk estimate
Statistics::Methodology
Sequential Monte Carlo
QA
Statistics - Methodology
Mathematics
Estimation theory
Applied Mathematics
State-space model
Estimator
Markov chain Monte Carlo
Agricultural and Biological Sciences (miscellaneous)
Statistics::Computation
Metropolis–Hastings algorithm
symbols
62F15
Statistics, Probability and Uncertainty
General Agricultural and Biological Sciences
Subjects
Details
- Language :
- English
- ISSN :
- 00063444
- Database :
- OpenAIRE
- Journal :
- Doucet, A, Pitt, M, Deligiannidis, G & Kohn, R 2015, ' Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator ', BIOMETRIKA, vol. 102, no. 2, pp. 295-313 . https://doi.org/10.1093/biomet/asu075
- Accession number :
- edsair.doi.dedup.....dd6508458d116956beda3b91b30b076f