Parallel Computing in Bayesian Inference

这项研究旨在将贝叶斯统计推理和决策理论与现代计算和数值方法相结合。研究计划的核心是使并行/分布式计算处理方法适应贝叶斯统计和决策理论中的问题。这项研究将有三个主要方向：1)贝叶斯方法的理论发展，2)并行/分布式计算算法的研究，3)数值技术在贝叶斯问题中的应用。为并行/分布式处理开发的方法、算法和软件将在广泛的理论和实践贝叶斯问题中发挥重要作用。应用领域将包括分层贝叶斯建模、灵敏度和稳健性、顺序分析及其在顺序过程控制中的应用、图像重建的贝叶斯方法以及神经网络的贝叶斯推理。

This research is designed to integrate Bayesian statistical inference and decision theory with modern computational and numerical methods. The core of the research program is the adaptation of methods for parallel/distributed processing of computation to problems in Bayesian statistics and decision theory. The research will have three principle directions: 1) theoretical development of the Bayesian methodology, 2) research into parallel/distributed computing algorithms, and 3) applications of numerical techniques to Bayesian problems. The methods, algorithms, and software to be developed for parallel/distributed processing will be important in a wide variety of theoretical and practical Bayesian problems. Areas of application will include hierarchical Bayesian modeling, sensitivity and robustness, sequential analysis with application in sequential process control, Bayesian methods for image reconstruction, and Bayesian inference for neural networks.