Estimation, Detection and Control of Multiple Change-point Stochastic Systems with Applications to Economics, Engineering, Biology and Climate Science

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The problems of parameter estimation, abrupt change detection, and system control in stochastic systems with multiple change-points arise in financial econometrics, industrial quality control, gene mapping and abrupt climate change studies. An important ingredient in the solution to these problems is efficient estimation of piecewise constant parameters with unknown multiple change-points. In the proposed research, the investigator will develop a unified hidden Markov filtering approach to parameter estimation, and bounded complexity approximation algorithms that can be implemented via parallel recursions. In particular, four types of problems from different fields are investigated in the study. The first develops estimation and forecasting procedures for an econometric time series model, in which a generalized autoregressive conditional heteroskedasticity process for conditional variances is intertwined with piecewise constant unconditional variances for which the change-points are unknown. The second studies detection of parameter changes with unknown pre- and post-change distributions in stochastic systems. The third investigates segmentation of piecewise constant signals in sequence data and discusses its applications to the analysis of genomic copy number variation. The fourth, arising in abrupt climate change, develops estimation theory and algorithms for multiple structural changes in the celebrated Lorenz system, which is chaotic. This system provides a highly simplified description of atmospheric circulation and has served as a testbed for methods of parameter estimation in climate studies. The investigator will show how these challenging problems from different areas are unified and solved by the hidden Markov filtering approach to multiple change-points.Abrupt or gradual parameters changes in complex stochastic systems are often encountered in various scientific and engineering practices including economics, biology and climate studies. While systems with gradually changing parameters have received much attention historically, recent advances in science and engineering show the growing importance of stochastic systems with abrupt, but unknown parameter changes. In economic studies, the authorities and industrial practitioners are interested in dating turning points of economic activities. In current genomic research, DNA copy number variations (i.e., gains or losses of specific chromosomal segments) are key genetic events in the development and progression of numerous diseases including cancer, HIV acquisition, and Alzheimer and Parkinson's disease, and an important step in studying these genetic events is to identify the regions of variations. In climate studies, abrupt changes of Earth's climate have attracted increasing attention from researchers and policy makers due to their projected severe impact on regional and global ecological and economic systems, and new statistical techniques are needed for nonstationary climate or climate-related variables due to the limited values of current statistical tools with a gradually changing assumption. However, the effort of solving these problems is hampered by the statistical and computational complexity caused by unknown abrupt changes. The proposed research presents a unified statistical theory to model and estimate such changes in complex systems, and the applications should shed new light on efforts at tackling these challenging problems. In particular, this study allows us to model abrupt changes of climate systems at the global level by incorporating current state-of-the-art climate modeling techniques with statistical analysis. Furthermore, the application of the proposed research to climate sciences links the statistical theory with high-performance computation, and hence opens up new horizons to statistical methodologies.