Mathematical Sciences: Sampling Based Methods for Bayesian Computation

边际后验密度的计算是贝叶斯推理应用于数据的一个重要组成部分。当密度被表示为极高维空间上的积分时，本研究涉及在计算这些密度时使用吉布斯抽样方法。所讨论的理论问题包括将“统一比率”抽样方法扩展到多变量分布以及期望的准确计算。还将讨论令人满意的收敛准则的发展。特别是，将寻求一种产生自动决策的正式方法。

The calculation of marginal posterior densities is an essential component of the application of Bayesian inference to data. This research involves the use of the method of Gibbs sampling in the computation of these densities when they are represented as integrals over spaces of extremely high dimension. Theoretical issues addressed include the extension of the "ratio of uniforms" method of sampling to multivariate distributions as well as accurate calculations of expectations. The development of satisfactory convergence criteria will also be attacked. In particular, a formal methodology that yields an automated decision will be sought.