Practical Perfect Sampling for Bayesian Computation and Engineering and Financial Applications

这是一个综合研究项目，旨在使完美或精确采样成为常见贝叶斯建模以及工程和金融应用的更实用的工具。当前精确采样受到限制的关键原因包括可用算法的不适用性，因为它们在不存在的假设（例如单调性或紧凑空间）下运行或假设不可用的元素（例如合适的“边界链”），以及许多提出的完美采样算法需要太长或太多内存才能超出某些“程式化”应用程序的实用性。研究人员建议充分利用常见应用中出现的特定问题结构来增强精确模拟算法的性能。更准确地说，在贝叶斯计算的背景下，研究人员研究了数据增强和多移位/缩放耦合器的思想，以实现和加速许多常见贝叶斯模型的完美采样算法。研究人员还提出了一种新的精确模拟算法，适用于随机建模（如在工程和金融领域）的应用，特别是对于定点随机方程解的分布。此外，研究人员还研究了实现基于再生的精确模拟算法的一般程序。最后，研究人员分析了相关方法，例如“近乎完美采样”，通过允许已知且受控的误差项，可以在速度和适用性方面提供可观的增益。马尔可夫链蒙特卡罗（MCMC）是一类非常流行的科学计算方法，完美采样是 MCMC 方法的子类，旨在提供更准确的结果。为这种更高的精度付出的代价是，构建完美采样算法通常是一项艰巨的任务。主要目的该提案的目的是研究减少此类困难的实用策略，从而使完美抽样成为比目前更实用的工具。研究人员所描述的完美抽样研究活动重点关注统计推断、生产和制造系统以及金融计量经济学中广泛使用的模型，因此，研究人员提出的研究计划也将极大地提高对完美抽样在实践中的适用性的一般知识和理解。由于学生研究助理的直接参与，以及通过研讨会和出版物，拟议的活动将通过研究和相关教学和建议，在统计计算实践和理论方面产生广泛的影响。

This is a comprehensive research project aimed at making perfect or exact sampling a more practical tool for common Bayesian modeling, as well as for engineering and financial applications. Key reasons for the current limitation of exact sampling include the non-applicability of available algorithms because they operate under assumptions that are not present (such as monotonicity or compact spaces) or assume elements that are not available (such as suitable ``bounding chains''), and the fact that many proposed perfect sampling algorithms take too long or too much memory to be practical beyond certain ``stylized'' applications. The investigators propose to take full advantage of specific problem structures arising in common applications to enhance the performance of exact simulation algorithms. More precisely, in the context of Bayesian computations, the investigators study the idea of data augmentation and multi-shift/scaling couplers to implement and to speed up perfect sampling algorithms for a number of common Bayesian models. The investigators also propose a new exact simulation algorithm that is suitable for applications in stochastic modeling (as in the contexts of engineering and finance), particularly for distributions that are solutions of fixed point stochastic equations. In addition, the investigators study a general procedure to implement a regeneration-based exact simulation algorithm. Finally, the investigators analyze related methods, such as ``nearly perfect sampling", which by allowing a known and controlled error term, can potentially provide considerable gain in terms of both speed and applicability.Markov chain Monte Carlo (MCMC) is a class of very popular methods for scientific computation, and Perfect Sampling is a subclass of MCMC methods that aim to deliver more accurate results. The price one pays for this better accuracy is that the construction of a Perfect Sampling algorithm is typically a difficult task. The main purpose of this proposal is to study practical strategies for reducing such difficulties and thereby to make Perfect Sampling a more practical tool than currently it is. The research activities on perfect sampling described by the investigators focus on widely used models in statistical inference, production and manufacturing systems and financial econometrics. Therefore, the research plan that the investigators propose can have a substantial impact in a great variety of applications in Statistics, Industrial Engineering and Finance. The proposed research activities will also greatly advance the general knowledge and understanding of the applicability of perfect sampling in practice thereby addressing a key problem in the MCMC methodology. The proposed activities will have broad impact in both statistical computation practice and theory, via both research and associated teaching and advising due to the direct involvement of student research assistants and via seminars and publications. The investigators will also make every effort possible to recruit the best research assistants who at the same time will also enhance diversity in their general research environment.