Bayesian Preposterior Simulation

9704934贝叶斯预后处理模拟彼得·米勒杜克大学我们将后验模拟方法和程序的范围扩展到期望效用最大化。主要工具是在增广概率模型中进行模拟。为了使期望效用最大化，将原始的关于参数和数据的概率模型扩充为关于决策变量、模型参数和数据的人工概率模型。选择增广概率模型，使得决策参数上的边际分布与期望效用成正比，从而该边际分布的模式对应于最优设计。基于这种辅助概率模型，我们发展了新的适合模拟的马尔可夫链蒙特卡罗方法，并研究了基于模拟蒙特卡罗样本的可能高维分布中的模式估计算法。贝叶斯框架通过问题构造、不确定性建模、偏好建模、期望效用最大化和敏感度分析的迭代循环为决策提供一致的支持。统计学中最近的计算发展(吉布斯抽样、随机替代抽样)极大地扩大了用于不确定性建模的模型范围。我们研究了这些方法在决策周期的其他部分的使用，特别是期望效用最大化和偏好建模。所研究的方法是基于模拟的和高度计算密集型的，需要最先进的计算机模拟，涉及到联邦高性能计算的战略领域。这项研究的影响是扩大了期望效用最大化即决策问题的形式解实际上是可行的问题的类别，类似于Gibbs抽样和相关技术如何使复杂的概率模型可用于不确定性建模。

DMS-9704934 BAYESIAN PREPOSTERIOR SIMULATION Peter Mueller Duke Univiversity We expand the ambit of methods and programs developed for posterior simulation to expected utility maximization. The main tool is simulation in an augmented probability model. For expected utility maximization the original probability model on parameters and data is augmented to an artificial probability model on decision variables, model parameters and data. The augmented probability model is chosen such that the marginal distribution on the decision parameters is proportional to expected utility, and thus the mode of this marginal distribution corresponds to the optimal design. We develop novel Markov chain Monte Carlo techniques amenable to simulation from this auxiliary probability model and investigate algorithms for mode estimation in a possibly high dimensional distribution based on a simulated Monte Carlo sample. The Bayesian framework provides coherent support for decision making through an iterative cycle of problem structuring, uncertainty modeling, preference modeling, expected utility maximization and sensitivity analysis. Recent computational developments in statistics (the Gibbs sampler, stochastic substitution sampling) have significantly widened the range of models used for uncertainty modeling. We study the use of these methods in other parts of the decision making cycle, in particular expected utility maximization and preference modeling. The investigated methods are simulation based and highly computational intensive and require state of the art computer simulation, relating to the Federal Strategic Area of high performance computing. The impact of the research is to widen the class of problems where expected utility maximization, i.e., formal solution of decision problems, is practically feasible in a way similar to how Gibbs sampling and related techniques have made complex probability models accessible for uncertainty model ing.