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Order selection for heterogeneous semiparametric hidden Markov models.

Yudan Zou1, Xinyuan Song1, Qian Zhao2

  • 1Department of Statistics, Chinese University of Hong Kong, Hong Kong, Hong Kong.

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Summary

This study introduces a Bayesian double penalization (BDP) method for analyzing complex longitudinal data using Hidden Markov Models (HMMs). The BDP procedure efficiently estimates parameters and determines the number of hidden states simultaneously, outperforming traditional methods.

Keywords:
Bayesian methoddouble penalizationdynamic heterogeneitylongitudinal datasemiparametric model

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Area of Science:

  • Statistics
  • Biostatistics
  • Machine Learning

Background:

  • Hidden Markov Models (HMMs) are crucial for analyzing longitudinal data with dynamic heterogeneity.
  • Conventional HMM analysis often requires pre-specifying the model order (number of hidden states), which is frequently unknown.
  • Existing methods for simultaneous order selection and parameter estimation are limited to homogeneous parametric models and can be computationally intensive.

Purpose of the Study:

  • To propose a novel Bayesian double penalization (BDP) procedure for simultaneous order selection and parameter estimation in heterogeneous semiparametric HMMs.
  • To address the computational challenges associated with determining the order of HMMs when prior information is lacking.

Main Methods:

  • Developed a Bayesian double penalization (BDP) procedure for heterogeneous semiparametric HMMs.
  • Introduced a new Markov chain Monte Carlo (MCMC) algorithm with an adjust-bound reversible jump strategy to handle order updating.
  • Evaluated the method through simulation studies and application to real-world data.

Main Results:

  • The proposed BDP procedure demonstrated robust performance in parameter estimation for HMMs.
  • The method significantly outperformed conventional criterion-based approaches in simulation studies.
  • The BDP procedure proved effective in analyzing complex longitudinal data, as shown by its application to Alzheimer's Disease Neuroimaging Initiative data.

Conclusions:

  • The Bayesian double penalization (BDP) procedure offers an effective solution for simultaneous order selection and parameter estimation in heterogeneous semiparametric HMMs.
  • The novel MCMC algorithm facilitates efficient analysis of HMMs with unknown orders.
  • This approach enhances the utility of HMMs for analyzing dynamic heterogeneity in longitudinal data, with demonstrated success in biomedical research.