[Show abstract][Hide abstract] ABSTRACT: Benchmark estimation is motivated by the goal of producing an approximation to a poste- rior distribution that is better than the empirical distribution function. This is accomplished by incorporating additional information into the construction of the approximation. We fo- cus here on generalized post-stratication , the most successful implementation of benchmark estimation in our experience. We develop generalized post-stratication for settings where the source of the simulation diers from the posterior which is to be approximated. This al- lows us to use the techniques in settings where it is advantageous to draw from a distribution dieren t than the posterior, whether this is for exploration of the data and/or model, for algorithmic simplicity, to improve convergence of the simulation or for improved estimation of selected features of the posterior. We develop an asymptotic (in simulation size) theory for the estimators, providing con- ditions under which central limit theorems hold. The central limit theorems apply both to an importance sampling context and to direct sampling from the posterior distribution. The asymptotic results, coupled with large sample (size of data) approximation results provide guidance on how to implement generalized post-stratication . The theoretical results also explain the gains associated with generalized post-stratication and the empirically observed robustness to cutpoints for the strata. We note that the results apply well beyond the setting of Markov chain Monte Carlo simulation.
Journal of the American Statistical Association 02/2006; 101(September):1175-1184. · 1.83 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: While studying various features of the posterior distribution of a vector-valued parameter using an MCMC sample, a subsample is often all that is available for analysis. The goal of benchmark estimation is to use the best available information, i.e. the full MCMC sample, to improve future estimates made on the basis of the subsample. We discuss a simple approach to do this and provide a theoretical basis for the method. The methodology and beneflts of benchmark estimation are illustrated using a well-known example from the literature. We obtain as much as an 80% reduction in MSE with the technique based on a 1-in-10 subsample and show that greater beneflts accrue with the thinner subsamples that are often used in practice.
Journal of Computational and Graphical Statistics. 01/2004; 13(3).