主 题：Hidden Markov models with an unknown number of hidden states具有未知隐藏状态数的隐马尔可夫模型

主讲人：香港中文大学宋心远教授

主持人：统计学院林华珍教授

时间：2023年7月2日（周日）上午9:30-10:30

举办地点：柳林校区弘远楼408会议室

主办单位：统计研究中心和统计学院 科研处

主讲人简介：

Xinyuan Song is a full professor and Chair in the Department of Statistics, The Chinese University of Hong Kong. Her research interests are latent variable models, Bayesian methods, survival analysis, nonparametric and semiparametric methods, and statistical computing. She serves/served as an associate editor for a number of international journals in Statistics and Psychometrics, including Biometrics, Electronic Journal of Statistics, Canadian Journal of Statistics, Statistics and Its Interface, Computational Statistics and Data Analysis, Statistical Theory and Related Fields, Psychometrika, Structural Equation Modeling: A Multidisciplinary Journal.

宋心远，香港中文大学统计学系正教授及系主任。主要研究方向为潜变量模型、贝叶斯方法、生存分析、非参数和半参数方法、统计计算等。担任或曾担任包括《Biometrics》《Electronic Journal of Statistics 》《Canadian Journal of Statistics》《Statistics and Its Interface》《Computational Statistics and Data Analysis》《Statistical Theory and Related Fields》《Psychometrika》 等多个国际期刊的副主编。

内容简介：

Hidden Markov models (HMMs) are valuable tools for analyzing longitudinal data due to their capability to describe dynamic heterogeneity. Conventional HMMs typically assume that the number of hidden states (i.e., the order of HMMs) is known or predetermined through criterion-based methods. This talk discusses double-penalized procedures for simultaneous order selection and parameter estimation for homogeneous and heterogeneous HMMs. We develop novel computing algorithms to address the challenges of updating the order. Furthermore, we establish the consistency of order and parameter estimators. Simulation studies show that the proposed procedures considerably outperform the commonly used criterion-based methods. An application to the Alzheimer's Disease Neuroimaging Initiative study further confirms the utility of the proposed method.

隐马尔可夫模型(HMMs)由于其描述动态异质性的能力而成为分析纵向数据的重要工具。传统的HMMs通常假设隐藏状态的数量(即HMMs的阶数)是已知的或通过基于准则的方法预先确定的。本次报告讨论了同质和异质HMMs同时进行阶数选择和参数估计的双重判罚方法。我们开发了新的计算算法来解决更新阶数的挑战。进一步，我们建立了阶估计和参数估计的一致性。模拟研究表明，所提出的方法大大优于常用的基于准则的方法。在阿尔茨海默病神经影像学倡议研究中的应用进一步证实了所提出方法的实用性。