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

复杂随机系统的突然结构变化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具有参数跳跃和有效推理程序的适当模型。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具有突变结构变化的三个复杂问题，并为此制定相应的统计方法。第一个是开发一个具有未知结构断裂的调制马尔可夫模型，以描述当经济经历突然的结构变化时美国公司的信用评级转变。本文还提出了一种推理程序来分析美国信贷市场的结构性变化与宏观经济和企业特定协变量的变化之间的关系。二是研究急剧变化环境下的学习和控制问题，提出了一种近似的政策优化和自适应控制方法，用于最优政策的分析，并讨论了其在货币政策分析中的应用。第三个问题是在染色质相互作用分析中建立一个分割模型来识别拓扑相关结构域，这是分析下一代基因组测序数据的重要一步。提出了一种统计上和计算上高效的分割算法来估计拓扑相关域的边界。PI将展示如何通过提出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理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的研究已经有了大量的文献，但是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限制，因此没有得到足够的重视。在当前的遗传研究中，了解三维染色体结构和染色质相互作用解码和解释基因组的功能可以为解码基因调控和维持基因组稳定性以及DNA复制，修复和修饰的机制提供重要线索，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拓扑相关结构域。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转变的潜在有害影响。在金融研究中，2008-2009年的金融危机向监管当局提出了迫切的需求，即应该基于可靠的统计和计量模型和程序来监测金融市场，因此应该建立一个早期预警系统来监测金融体系的稳定性。拟议的研究探讨建立定量和可执行的金融危机早期预警系统的可能性，该系统汇总来自个别公司的微观经济信息和来自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.