Bayesian Analysis of Proportions via a Hidden Markov Model


CAN C. E. , Ergun G., Soyer R.

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s11009-022-09971-0
  • Journal Name: METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
  • Journal Indexes: Science Citation Index Expanded, Scopus, ABI/INFORM, Business Source Elite, Business Source Premier, INSPEC, zbMATH
  • Keywords: Hidden Markov Model, Proportions, Beta distribution, Gibbs Sampling, Metropolis-Hastings algorithm, BETA REGRESSION-MODELS, TIME-SERIES, LIKELIHOOD, DISPERSION, MIXTURE

Abstract

Time series of proportions arise in many contexts. In this paper, we consider a hidden Markov model (HMM) to describe temporal dependence in such series. In so doing, we introduce a Beta-HMM and develop its Bayesian analysis using Markov Chain Monte Carlo Methods (MCMC). Our proposed model is based on a conjugate prior for beta likelihood which enables us develop Bayesian posterior and predictive computations in an efficient manner. We also address the problem of assessing dimension of the HMM using the marginal likelihood of the model which can be evaluated using posterior samples. Finally, we implement our model and the Bayesian methodology using weekly data on market shares.