Mathematical Sciences: Sampling Based Methods for Bayesian Computation

边缘后验密度的计算是一个 贝叶斯推理应用的基本组成部分， 数据 本研究采用吉布斯方法 在计算这些密度时， 表示为在极高维空间上的积分。 所涉及的理论问题包括“比率”的扩展 多变量分布的均匀抽样方法 以及对期望值的精确计算。发展 令人满意的收敛标准也将受到攻击。 在 特别是，一个正式的方法，产生一个自动化的 将寻求决定。

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.