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

TY - JOUR

T1 - Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator

AU - Doucet, A.

AU - Pitt, Mike

AU - Deligiannidis, George

AU - Kohn, R.

PY - 2015/6

Y1 - 2015/6

N2 - 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.

AB - 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.

KW - Intractable likelihood

KW - Metropolis-Hastings algorithm

KW - Particle filter

KW - Sequential Monte Carlo

KW - State-space model

UR - http://www.scopus.com/inward/record.url?scp=84929220466&partnerID=8YFLogxK

U2 - 10.1093/biomet/asu075

DO - 10.1093/biomet/asu075

M3 - Article

AN - SCOPUS:84929220466

SN - 0006-3444

VL - 102

SP - 295

EP - 313

JO - BIOMETRIKA

JF - BIOMETRIKA

IS - 2

ER -