Abstract
Sequential Monte Carlo methods, also known as particle filters, provide tractable estimates of the latent states in complex hidden Markov models (HMMs) and have been widely used in many applications, ranging from computational biology to engineering and finance. In this talk the speaker addresses two long-standing problems related to particle filters. One is related to estimation of the standard errors of the Monte Carlo estimates. Since the simulated trajectories (particles) are dependent ("interacting particles"), classical standard error formulas are no longer applicable. By making use of martingale theory, he derives consistent estimates of the standard errors of particle filters. Another problem is related to unknown parameters in the HMMs. In practical applications, HMMs usually have unspecified parameters that are to be estimated from the observations. These parameters can be regarded as states in a Bayesian framework, but since they do not undergo dynamics, they often lead to degeneracy of the augmented particle filter. His attempt to address this problem has led to a new approach to MCMC, which can combine with particle filters to derive adaptive particle filters that do not have the degeneracy problem and are also analytically tractable, yielding consistent standard error estimates. Applications to dynamic frailty models in credit risk analytics of joint defaults of multiple firms and to SLAM (Simultaneous Localization and Mapping) algorithms in robotics are given to illustrate the results.
About the speaker
Prof Tze Leung Lai received his PhD in Mathematical Statistics from Columbia University in 1971. He stayed on the faculty until he moved to Stanford University in 1987, where he is currently Professor of Statistics, of the Institute for Computational and Mathematical Engineering, and by courtesy, of Health Research and Policy. He is also Director of Financial Mathematics Program and the Financial and Risk Modeling Institute at Stanford, and Co-director of the Biostatistics Core of the Cancer Institute and the Center of Innovative Design at the School of Medicine.
Prof Lai won the Committee of Presidents of Statistical Societies Award in 1983 and the Abraham Wald Prize in Sequential Analysis in 2005. He is an elected Member of Academia Sinica, where he has been an Advisory Committee member of the Institute of Statistical Science since 1992. He is also an Advisory Committee member of the Department of Statistics and Actuarial Science and of the Institute for Mathematical Research at The University of Hong Kong, and of the Statistics Center at Peking University and the Mathematical Sciences Center at Tsinghua University.
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