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出现在科学和工程领域，包括经济学、金融学、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适当的模型参数跳跃和有效的推理程序。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具有突然结构变化的复杂问题，并为它们开发相应的统计方法。第一个是开发一个具有未知结构突变的调制马尔可夫模型，以描述美国企业在经济发生突然结构变化时的信用评级转变。本文还提出了一个推理程序，以分析美国信贷市场结构变化与宏观经济和企业特定协变量变化之间的关系。二是研究了急剧变化环境下的学习与控制问题，提出了一种近似的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个分割模型，在染色质相互作用的分析中识别拓扑相关的结构域，这是下一代基因组测序数据分析中的重要一步。一个统计和计算效率的分割算法也提出了估计拓扑相关域的边界。PI将展示如何通过拟议的统计模型和推理程序来统一和解决不同领域的这些具有挑战性的问题。具有突然结构变化的复杂随机系统中的统计推断问题出现在科学和工程中，包括经济学，金融，风险管理，遗传学，工业质量控制和公共卫生。对于具有简单结构变化机制的随机系统，已有大量的文献进行了研究，然而，具有突变结构的复杂随机系统的问题由于其统计困难而受到阻碍，因此没有得到太多的关注。在目前的遗传学研究中，了解染色体的三维结构和染色质相互作用，以解码和解释基因组的功能，可以提供重要的线索，对解码基因调控和基因组稳定性的维护机制，以及DNA复制，修复和修改，在研究这些遗传事件的重要一步是确定拓扑结构相关的结构域从染色质架构数据。在宏观经济研究中，中央银行热衷于控制政策目标，并在存在不可观察的经济结构性断裂的同时估计政策行动的影响，以便采取适当的货币和财政政策来减轻经济急剧变化的潜在有害影响。在金融研究方面，2008-2009年的金融危机提出了监管当局的迫切需要，即应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，因此应建立预警系统，以监督金融体系的稳定性。拟议的研究探讨了建立定量和可实施的金融危机预警系统的可能性，该系统汇总了单个企业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.