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Bayesian quantile nonhomogeneous hidden Markov models.

Hefei Liu1, Xinyuan Song2, Yanlin Tang3

  • 1School of Statistics, Capital University of Economics and Business, Beijing, China.

Statistical Methods in Medical Research
|July 30, 2020
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Summary
This summary is machine-generated.

This study introduces a quantile hidden Markov model for analyzing longitudinal data, focusing on the entire response distribution. This flexible approach, applied to a cocaine use study, offers new insights into prevention strategies.

Keywords:
Asymmetric Laplace distributionBayesian analysishidden Markov modelnonhomogeneous transitionquantile regression

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Traditional hidden Markov models (HMMs) primarily analyze the mean of longitudinal responses.
  • The tails of the response distribution are crucial in many research areas but often overlooked by existing HMMs.
  • A need exists for methods that analyze the complete conditional distribution of responses within HMM frameworks.

Purpose of the Study:

  • To propose a quantile hidden Markov model (QHMM) for comprehensive analysis of longitudinal data.
  • To extend HMMs by allowing transition probabilities to depend on covariates, creating nonhomogeneous Markov chains.
  • To provide a flexible statistical framework for examining the entire conditional distribution of responses.

Main Methods:

  • Development of a Bayesian approach for statistical inference within the QHMM framework.
  • Utilization of efficient Markov chain Monte Carlo (MCMC) methods for parameter estimation.
  • Simulation studies to evaluate the empirical performance and robustness of the proposed QHMM.

Main Results:

  • The proposed QHMM systematically examines the entire conditional distribution of the response.
  • Nonhomogeneous Markov chains offer greater flexibility compared to homogeneous HMMs.
  • The methodology was successfully applied to a real-world cocaine use study.

Conclusions:

  • The quantile hidden Markov model provides a powerful tool for analyzing complex longitudinal data.
  • This approach offers new insights into understanding and preventing behaviors like cocaine use.
  • The QHMM framework enhances the flexibility and scope of hidden Markov modeling.