Abrupt Structural Changes in Complex Stochastic Systems with Applications to Economics, Finance, and Genetics

复杂随机系统的结构突变发生在科学和工程领域，包括经济、金融、遗传学、工业质量控制和公共卫生。分析这些问题的一个重要步骤是开发具有参数跳跃和有效推理过程的适当模型。在拟议的研究中，首席研究员将调查最近在三个不同学科中出现的三个结构突变的复杂问题，并为它们制定相应的统计方法。首先是开发一个结构突变未知的调制马尔可夫模型，以表征当经济经历突然的结构变化时美国公司的信用评级变化。本文还提出了一种分析美国信贷市场结构变化与宏观经济变量和特定企业协变量变化之间关系的推理程序。二是研究急剧变化环境下的学习与控制问题，提出了一种用于分析最优政策的近似政策优化和自适应控制方法，并讨论了其在货币政策分析中的应用。第三个问题是开发一种分割模型，在染色质相互作用的分析中识别拓扑相关的结构域，这是分析下一代基因组测序数据的重要步骤。文中还提出了一种统计上和计算上有效的分割算法来估计拓扑相关区域的边界。PI将展示如何通过拟议的统计模型和推理程序统一和解决不同领域的这些具有挑战性的问题。结构突变的复杂随机系统中的统计推断问题出现在科学和工程领域，包括经济学、金融学、风险管理、遗传学、工业质量控制和公共卫生。关于具有简单结构变化机制的随机系统已经有了大量的文献，然而，具有结构突变的复杂随机系统的问题一直受到统计困难的阻碍，因此没有得到太多的关注。在目前的遗传学研究中，了解三维染色体结构和染色质相互作用以解码和解释基因组的功能，可以为破译基因调控机制、维持基因组稳定性以及DNA复制、修复和修饰提供重要线索，研究这些遗传事件的重要步骤是从染色质结构数据中识别与拓扑相关的结构域。在宏观经济研究中，各国央行热衷于在出现不可观察到的经济结构突变的同时，控制政策目标并估计政策行动的影响，以便能够采取适当的货币和财政政策，以减轻经济急剧转向的潜在有害影响。在金融研究中，2008-2009年金融危机使监管当局迫切需要根据可靠的统计和计量经济学模型和程序对金融市场进行监测，因此应建立一个早期预警系统来监测金融系统的稳定性。拟议的研究探讨了建立量化和可实施的金融危机预警系统的可能性，该系统汇总了个别公司的微观经济信息和一般经济活动的宏观经济统计数据。

Abrupt structural changes in complex stochastic systems arise in science and engineering, including economics, finance, genetics, industrial quality control, and public health. An important step to analyze these problems is to develop appropriate models with parameter jumps and efficient inference procedures. In the proposed research, the principal investigator will investigate three complicated problems with abrupt structural changes that recently arise in three different disciplines and develop corresponding statistical methodology for them. The first is to develop a modulated Markov model with unknown structural breaks to characterize U.S. firms' credit rating transitions when the economy undergoes abrupt structural changes. An inference procedure is also proposed to analyze the relationship between structural changes in the U.S. credit market and variations of macroeconomic and firm-specific covariates. The second is to investigate the issue of learning and control in a sharply changing environment and develop an approximate policy optimization and adaptive control method for the analysis of optimal policies, its application to monetary policy analysis is also discussed. The third problem is to develop a segmentation model that identifies topologically associated domains in the analysis of chromatin interactions, which is an important step in the analysis of the next-generation genome-sequencing data. A statistically and computationally efficient segmentation algorithm is also proposed to estimate the boundaries of topologically associated domains. The PI will show how these challenging problems in different areas can be unified and resolved by the proposed statistical models and inference procedures. Statistical inference problems in complex stochastic systems with abrupt structural changes arise in science and engineering, including economics, finance, risk management, genetics, industrial quality control, and public health. There has been an extensive literature on stochastic systems with simple structural change mechanisms, however, problems of complex stochastic systems with abrupt structural changes have been hampered by their statistical difficulty and hence has not received much attention. In current genetic research, understanding 3D chromosomal structures and chromatin interactions for decoding and interpreting functions of the genome can provide important hints toward decoding the mechanisms of gene regulation and the maintenance of genome stability, as well as DNA replication, repair and modification, an important step in studying these genetic events is to identify the topologically associated domains from chromatin architecture data. In macroeconomic studies, central banks are keen to control the policy target and estimate the impact of policy action simultaneously with the presence of the unobservable economic structural breaks, so that proper monetary and fiscal policies can be taken to mitigate the potential harmful impact of sharp economic turns. In financial studies, the 2008-2009 financial crisis raises the immediate needs for the regulatory authorities that the financial market should be monitored based on solid statistical and econometric models and procedures, and hence an early warning system should be established to surveillance the stability of financial systems. The proposed research explores the possibility of building quantitative and implementable early-warning systems for financial crisis, which aggregates microeconomic information from individual firms and macroeconomic statistics from general economic activities.