Williams, Brian J.; Huzurbazar, Aparna V. Posterior sampling with constructed likelihood functions: an application to flowgraph models. (English) Zbl 1114.62027 Appl. Stoch. Models Bus. Ind. 22, No. 2, 127-137 (2006). The authors consider posterior sampling in situations where data are incomplete in such a way that likelihood functions corresponding to portions of the data must be constructed. Such situations arise in the modelling of time-to-event data when not all of the event occurrences are observed. The estimation of Bayesian predictive distributions for flowgraph models using Laplace transform inversion and slice sampling techniques are described. The authors construct likelihood functions for the incomplete data and use them in a Markov chain Monte Carlo algorithm to sample from the approximate posterior and compute Bayes predictive distributions. A real data example for a cellular telephone network is used. Reviewer: Aleksandr D. Borisenko (Kyïv) Cited in 1 Document MSC: 62F15 Bayesian inference 65C40 Numerical analysis or methods applied to Markov chains 62P30 Applications of statistics in engineering and industry; control charts Keywords:Bayesian predictive distribution; censored data; flowgraph model; incomplete data; slice sampling; queuing model PDFBibTeX XMLCite \textit{B. J. Williams} and \textit{A. V. Huzurbazar}, Appl. Stoch. Models Bus. Ind. 22, No. 2, 127--137 (2006; Zbl 1114.62027) Full Text: DOI References: [1] West, The Statistician 43 pp 31– (1994) [2] Huzurbazar, Technometrics 42 pp 300– (2000) [3] Flowgraph Models for Multistate Time-to-Event Data. Wiley: New York, 2005. · Zbl 1055.62123 [4] Saddlepoint Approximation. Oxford Press: New York, 1995. [5] Abate, Queuing Systems 10 pp 5– (1992) [6] . A First Course in Stochastic Processes. Academic Press: New York, 1975. [7] . Semi-Markov Processes and Reliability. Birkhauser: Boston, 2001. · Zbl 0990.60004 · doi:10.1007/978-1-4612-0161-8 [8] Barnett, Journal of Computational and Graphical Statistics 9 pp 759– (2000) [9] Huzurbazar, Communications in Statistics: Simulation and Computation 34 pp 113– (2005) [10] , , . Bayesian Data Analysis. Chapman & Hall/CRC: Florida, 1995. [11] Neal, Annals of Statistics 31 pp 705– (2003) [12] . Bayes and Empirical Bayes Methods for Data Analysis (2nd edn). Chapman & Hall: Boca Raton, FL, 2000. · Zbl 1017.62005 · doi:10.1201/9781420057669 [13] Mobile Cellular Telecommunications: Analog and Digital Systems. McGraw-Hill: New York, 1995. [14] . An Introduction to Stochastic Modelling. Academic Press: Orlando, 1984. [15] . Strategies for improving MCMC. In Markov Chain Monte Carlo in Practice, , (eds). Chapman & Hall: London, 1996; 89–114. · Zbl 0844.62100 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.