Estimating discrete Markov models from various incomplete data schemes

  • Authors:
  • Alberto Pasanisi;Shuai Fu;Nicolas Bousquet

  • Affiliations:
  • EDF R&D, Industrial Risk Management Department, 6 quai Watier, 78401 Chatou, France;EDF R&D, Industrial Risk Management Department, 6 quai Watier, 78401 Chatou, France and University of Paris-Sud 11, Mathematics Department, Bat. 425, 91405 Orsay, France;EDF R&D, Industrial Risk Management Department, 6 quai Watier, 78401 Chatou, France

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2012

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Abstract

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a case, the estimation of transition probabilities is straightforwardly made by counting one-step moves from a given state to another. In many real-life problems, however, the inference is much more difficult as state sequences are not fully observed, namely the state of each individual is known only for some given values of the time variable. A review of the problem is given, focusing on Monte Carlo Markov Chain (MCMC) algorithms to perform Bayesian inference and evaluate posterior distributions of the transition probabilities in this missing-data framework. Leaning on the dependence between the rows of the transition matrix, an adaptive MCMC mechanism accelerating the classical Metropolis-Hastings algorithm is then proposed and empirically studied.