Posterior simulation via the exponentially tilted signed root log-likelihood ratio

Abstract

We explore the use of importance sampling based on exponentially tilted signed root log-likelihood ratios for Bayesian computation. Approximations based on exponentially tilted signed root log-likelihood ratios are used in two distinct ways; firstly, to define an importance function with antithetic variates and, secondly, to define suitable control variates for variance reduction. These considerations give rise to alternative simulation-consistent schemes to other importance sampling techniques (for example, conventional and/or adaptive importance sampling) for Bayesian computation in moderately parameterized regular problems. The schemes based on control variates can also be viewed as usefully supplementing computations based on asymptotic approximations by supplying external estimates of error. The methods are illustrated by a censored regression model and a more challenging 12-parameter nonlinear repeated measures model for bacterial clearance.