Determine the Number of States in Hidden Markov Models via Marginal Likelihood

报告题目：Determine the Number of States in Hidden Markov Models via Marginal Likelihood

报告人： 傅承德教授（中央大学）

时间：2023年04月07日（星期五）上午16:00-

地点：紫金港校区海纳苑2幢205教室

摘要：Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of hidden states for an HMM is a model selection problem, which is yet to be satisfactorily solved, especially for the popular Gaussian HMM with heterogeneous covariance. In this paper, we propose a consistent method for determining the number of hidden states of HMM based on the marginal likelihood, which is obtained by integrating out both the parameters and hidden states. Moreover, we show that the model selection problem of HMM includes the order selection problem of finite mixture models as a special case. We give a rigorous proof of the consistency of the proposed marginal likelihood method, and provide an efficient computation method for practical implementation. We numerically compare the proposed method with the Bayesian information criterion (BIC), demonstrating the effectiveness of the proposed marginal likelihood method.

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联系人: 庞天晓 txpang@zju.edu.cn

报告人简介：傅承德教授曾获中央大学数学系学士学位、南伊利诺伊大学数学硕士学位，并于1989年获得美国爱荷华州立大学统计与数学双博士学位。傅教授学术成果丰硕，发表在诸多领域的顶级学术期刊上，例如The Annals of Statistics、Biometrika 、Operations Research 、IEEE Transactions on Signal Processing、IEEE Trans. Inform. Theory、Quantitative Finance 等。他的研究领域包括计量金融学、金融时间序列、数值模拟和重要性抽样、马尔可夫模型之极限定理与变点检测、隐马尔可夫模型之统计推断等。1989年至2006年，傅教授分别担任台湾中央研究院统计科学研究所副研究员与研究员，并于2006年起担任中央大学统计研究所讲座教授。除此之外，他还是多所知名大学的客座教授，包括斯坦福大学、加州伯克利大学、哥伦比亚大学、上海交通大学、新加坡国立大学等。