Mathematical Sciences: Bayesian Computations

贝叶斯分析的分析方法依赖于“后验分布”作为对数据观察所积累的信息的表示。对于许多观察性研究以及许多或大多数实验情况，适当的分析取决于以令人满意的方式表示复杂的信息。计算技术的进步，特别是自适应蒙特卡罗积分，已经开始使重建合适的后验分布成为可能。这项研究将扩展现有方法的范围，包括通过结合分位数积分来提高效率，以及通过将分布近似问题表述为混合分布，然后实施聚类方法来提高效率。

Analytic methods for Bayesian analysis hinge upon the "posterior distribution" as the representation for the accumulated information upon observation of the data. For many observational studies as well as many or most experimental situations, an adequate analysis depends on representing complicated information in a satisfactory way. Advances in computational techniques, notably adaptive Monte-Carlo integration, have begun to make the reconstruction of suitable posterior distributions possible. This research will extend the range of existing methods both by incorporating quantile integration to increase efficiency and by formulating the distribution approximation problem in terms of mixture distributions and then imposing a clustering approach to gain efficiency.