报告地点：精正楼307

报告人：周洁 副教授（首都师范大学）

报告摘要：Hidden Markov models (HMMs) describe the relationship between two stochastic processes, namely, an observed outcome process and an unobservable finite-state transition process. Given their ability to model dynamic heterogeneity, HMMs are extensively used to analyze heterogeneous longitudinal data. A majority of early developments in HMMs assume that observation times are discrete and regular. This assumption is often unrealistic in substantive research settings where subjects are intermittently seen and the observation times are continuous or not predetermined. However, available works in this direction are few and restricted only to certain special cases, and assumed a  homogeneous generating matrix for the Markov process. Moreover, early developments have mainly assumed that the number of hidden states of an HMM is fixed and predetermined based on the knowledge of the subjects or a certain criterion. This approach determines the number of hidden states on a pairwise basis, which becomes increasingly tedious when the state space is enlarged. In this article, we consider a general continuous-time HMM with a covariate specific generating matrix and an unknown number of hidden states. The proposed model is highly flexible, thereby enabling it to accommodate different types of longitudinal data that are regularly, irregularly, or continuously collected. We develop a maximum likelihood approach along with an efficient computer algorithm for parameter estimation. We propose a new penalized procedure to select the number of hidden states. The asymptotic properties of the parameter and estimators of the number of hidden states are established. Various satisfactory features, including the finite sample performance of the proposed methodology, are demonstrated through simulation studies. The application of the proposed model to a dataset of bladder tumors is presented.

报告人介绍：周洁，副教授，首都师范大学99905银河在线登录平台。主要从事生存分析、复发事件与纵向数据的研究，在JASA，Biometrics, Statistica Sinica等国内外重要统计学杂志上发表SCI论文20余篇，主持多项北京市科研项目以及2项国家自然科学基金项目。