Practical Perfect Sampling for Bayesian Computation and Engineering and Financial Applications

这是一个全面的研究项目，旨在使完美或精确的采样成为普通贝叶斯建模以及工程和金融应用的更实用的工具。目前限制精确采样的主要原因包括现有算法的不适用性，因为它们是在不存在的假设下操作的（例如单调性或紧空间）或假设不可用的元素（例如合适的“绑定链”），以及许多提出的完美采样算法需要太长或太多的存储器，以至于超出某些“风格化”应用的实用性。研究人员建议充分利用常见应用中出现的特定问题结构，以提高精确仿真算法的性能。更确切地说，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/缩放耦合器的想法，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，该算法适用于随机建模（如工程和金融领域），特别是不动点随机方程解的分布。此外，研究人员研究了一个一般的程序来实现基于再生的精确模拟算法。最后，研究人员分析了相关的方法，如“近乎完美的抽样”，通过允许已知和受控的误差项，可以在速度和适用性方面提供相当大的增益。马尔可夫链蒙特卡罗（MCMC）是一类非常流行的科学计算方法，完美抽样是MCMC方法的一个子类，旨在提供更准确的结果。这种更好的精度所付出的代价是，完美采样算法的构建通常是一项艰巨的任务。本提案的主要目的是研究减少此类困难的实用策略，从而使完美采样成为比目前更实用的工具。研究人员所描述的关于完美抽样的研究活动集中在统计推断、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可以在统计学，工业工程和金融领域的各种应用中产生重大影响。拟议的研究活动也将大大推进一般知识和完美的抽样在实践中的适用性的理解，从而解决MCMC方法中的一个关键问题。 由于学生研究助理的直接参与以及研讨会和出版物，拟议的活动将通过研究和相关的教学和建议，对统计计算实践和理论产生广泛影响。研究人员还将尽一切努力招聘最好的研究助理，他们同时也将加强一般研究环境的多样性。

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.