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

Phelan, Michael J.

Ann. Stat. 18, No. 2, 603-616 (1990).

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

Keywords:

Bayes nonparametric estimation; Markov renewal process; conjugate class of a priori distributions; parameter space of semi-Markov transition distributions; Dirichlet family of distributions; random Markov matrices; Beta family of Lévy processes; random cumulative hazard functions; posterior law