Bayes Estimation from a Markov Renewal Process
The Annals of Statistics · 1990 · Volume 18 · Issue 2
Abstract
A procedure for Bayes nonparametric estimation from a Markov renewal process is developed. It is based on a conjugate class of a priori distributions on the parameter space of semi-Markov transition distributions. The class is characterized by a Dirichlet family of distributions for random Markov matrices and a Beta family of Levy processes for random cumulative hazard functions. The main result is the derivation of the posterior law from an observation of the Markov renewal process over a period of time.
Keywords
62C99, 62G05, 62M02, Bayes nonparametric estimation, Beta processes, Dirichlet, Markov renewal process
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