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

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.

34 pages, 9 figures, 3 tables

References in corpus (3)

• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• Martingale approximations for sums of stationary processes
• Positivity of hit-and-run and related algorithms

Cited by in corpus (4)

• Bayesian computation: a perspective on the current state, and sampling backwards and forwards
• Bayesian inference for Markov jump processes with informative observations
• Approximate Bayesian Computation for a Class of Time Series Models
• Approximate Inference for Observation Driven Time Series Models with Intractable Likelihoods