Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator

• 成果类型: Article
• 署名作者: Doucet, A.; Pitt, M. K.; Deligiannidis, G.; Kohn, R.
• 署名单位: University of Oxford; University of Warwick; University of New South Wales Sydney
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asu075
• 发表日期: 2015
• 页码: 295313
• 关键词: metropolis algorithms; CONVERGENCE; hastings

摘要

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.