Mathematical Sciences: Sampling Based Methods for Bayesian Computation

边际后验密度的计算是贝叶斯推断应用于数据的重要组成部分。这项研究涉及使用Gibbs抽样的方法来计算这些密度，当它们被表示为极高维空间上的积分时。所涉及的理论问题包括将抽样的“一致性比率”方法扩展到多变量分布以及预期的准确计算。令人满意的趋同标准的制定也将受到攻击。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.