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Bayes estimation from a Markov renewal process. (English) Zbl 0703.62086

Summary: 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 Lévy 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.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62G05 Nonparametric estimation
62C99 Statistical decision theory
60K15 Markov renewal processes, semi-Markov processes
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