This paper proposes an MCMC (Markov chain Monte Carlo) algorithm for estimating continuous phasetype distributions (CPHs). In Bayes estimation, it is well known that MCMC is one of the most useful and practical methods. The concrete MCMC algorithm for CPHs was developed by using Markov jump processes by Bladt et al. (2003). However, the existing MCMC algorithm spends much computation time in some cases. In this paper, we propose a new sampling algorithm which is based on uniformization technique and backward likelihood computation. The proposed algorithm is easier to implement and is more efficient in terms of computation time than the existing method.
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