This study develops parametric and semiparametric hidden Markov models to analyze univariate and multivariate longitudinal data. The proposed models generalize conventional regression models to allow bidirectional transition between hidden states and conventional hidden Markov models to allow latent variables and functional covariate effects. We develop maximum likelihood and Bayesian approaches, along with efficient Markov chain Monte Carlo algorithm, to conduct parameter estimation. The asymptotic properties of the parameter estimators are established. The proposed methodologies are applied to the analysis of two real-life datasets concerning the prevention of cocaine use and the risk factors of Alzheimer’ disease.

报告人简历: 宋心远，香港中文大学统计学系教授，系主任，主要研究方向包括潜变量模型，非参数和半参数回归，贝叶斯方法，生存分析及统计诊断等。宋心远教授于2000年在香港中文大学获得统计学博士学位，2001-2003年在中文大学从事统计博士后研究，2004年到至今任中文大学助理教授，副教授，教授。迄今为止,在国际著名的统计学及应用数学类期刊发表100多篇高水平学术论文。担任或曾经担任《Biometrics》、《Psychometrika》、《Structural Equation Modeling - A Multidisciplinary Journal》、《Computational Statistics and Data Analysis》、《Journal of the Korean Statistical Society》及《Statistical Theory and Related Fields》等多个国际期刊的副主编。