Importance-Weighted Marginal Bayesian Posterior Density Estimation
- 1 September 1994
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 89 (427) , 818-824
- https://doi.org/10.2307/2290907
Abstract
Markov chain sampling schemes generate dependent observations {Θi, 0 ≤ i ≤ n} from a full joint posterior distribution π(θdata). Frequently, only certain marginals of this full posterior density are of interest; thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations {Θi, 0 ≤ i ≤ n} from π(θ data). We propose a new importance-weighted marginal density estimation (IWMDE) method. An IWMDE is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w. The asymptotic properties for the IWMDE and the guidelines for choosing a weighting conditional density w are also considered. A bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the IWMDE's for the marginal posterior densities.Keywords
This publication has 1 reference indexed in Scilit:
- Bayesian Analysis of Constrained Parameter and Truncated Data Problems Using Gibbs SamplingJournal of the American Statistical Association, 1992