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.
@article{1176347618,
author = {Phelan, Michael J.},
title = {Bayes Estimation from a Markov Renewal Process},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 603-616},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347618}
}
Phelan, Michael J. Bayes Estimation from a Markov Renewal Process. Ann. Statist., Tome 18 (1990) no. 1, pp. 603-616. http://gdmltest.u-ga.fr/item/1176347618/