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Bayesian analysis of elapsed times in continuous-time Markov chains. (English) Zbl 1153.62019

Summary: The authors consider Bayesian analysis for continuous-time Markov chain models based on a conditional reference prior. For such models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition, an infinitesimal rate matrix also characterizes this class of models.
Exports often have good prior knowledge about the parameters of this matrix. The authors show that he use of a proper prior for the rate matrix parameters together with the conditional reference prior for the elapsed time yields a proper posterior distribution. The authors also demonstrate that, when compared to analyses based on priors previously proposed in the literature, a Bayesian analysis on the elapsed time based on the conditional reference prior possesses better frequentist properties. The type of prior thus represents a better default prior choice for estimation software.

MSC:

62F15 Bayesian inference
62M05 Markov processes: estimation; hidden Markov models

Software:

MrBayes; PHYLIP
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Full Text: DOI

References:

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