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Keywords:
Bayesian inference; fault diagnostics; Poisson processes; reversible-jump MCMC
Bayesian inference; fault diagnostics; Poisson processes; reversible-jump MCMC
Summary:
The problem of identifying the source from observations from a Poisson process can be encountered in fault diagnostics systems based on event counters. The identification of the inner state of the system must be made based on observations of counters which entail only information on the total sum of some events from a dual process which has made a transition from an intact to a broken state at some unknown time. Here we demonstrate the general identifiability of this problem in presence of multiple counters.
References:
[1] Chen, Ming-Hui, Shao,, Qi-Man, Ibrahim J. Q.: Monte Carlo Methods in Bayesian Computation. Springer, New York 2000 MR 1742311 | Zbl 0949.65005
[2] Geman S., Geman D.: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence 64 (1984), 2, 721–741 DOI 10.1109/TPAMI.1984.4767596 | Zbl 0573.62030
[3] Green P.: Reversible jump Markov chain Monte Carlo computation, Bayesian model determination. Biometrika 82 (1995), 711–732, http://www.stats.bris.ac.uk/pub/reports/MCMC/revjump.ps DOI 10.1093/biomet/82.4.711 | MR 1380810
[4] Marrs A. D.: An application of Reversible–Jump MCMC to multivariate spherical Gaussian mixtures. In: Advances in Neural Information Processing Systems 10 (M. I. Jordan, M. J. Kearns, and S. A. Solla, eds.), MIT Press, Cambridge, MA 1998
[5] Neal R. M.//Probabilistic Inference Using Markov Chain Monte Carlo Methods: Technical Report No. CRG-TR-93-1, Dept. of Computer Science, University of Toronto, 1993, ftp:. ftp.cs.toronto.edu/pub/radford/review.ps.Z
[6] Robert C. P., Casella G.: Monte Carlo Statistical Methods. Springer–Verlag, New York 1999 MR 1707311 | Zbl 1096.62003
[7] Viallefont V., Richardson, S., Green P.: Bayesian analysis of Poisson mixtures. J. Nonparametric Statistics 14 (2002), 1-2, 181–202 DOI 10.1080/10485250211383 | MR 1905593 | Zbl 1014.62035
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