Geodesic
Reversible jump MCMC for two-state multivariate Poisson mixtures
Kybernetika, Tome 39 (2003) no. 3, pp. 307-315 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 62F15, 62M05, 62P30, 65C40
Keywords: Bayesian inference; fault diagnostics; Poisson processes; reversible-jump MCMC 
@article{KYB_2003_39_3_a6,
     author = {Lahtinen, Jani and Lampinen, Jouko},
     title = {Reversible jump {MCMC} for two-state multivariate {Poisson} mixtures},
     journal = {Kybernetika},
     pages = {307--315},
     year = {2003},
     volume = {39},
     number = {3},
     mrnumber = {1995735},
     zbl = {1249.62009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a6/}
}
TY  - JOUR
AU  - Lahtinen, Jani
AU  - Lampinen, Jouko
TI  - Reversible jump MCMC for two-state multivariate Poisson mixtures
JO  - Kybernetika
PY  - 2003
SP  - 307
EP  - 315
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a6/
LA  - en
ID  - KYB_2003_39_3_a6
ER  - 
%0 Journal Article
%A Lahtinen, Jani
%A Lampinen, Jouko
%T Reversible jump MCMC for two-state multivariate Poisson mixtures
%J Kybernetika
%D 2003
%P 307-315
%V 39
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a6/
%G en
%F KYB_2003_39_3_a6
Lahtinen, Jani; Lampinen, Jouko. Reversible jump MCMC for two-state multivariate Poisson mixtures. Kybernetika, Tome 39 (2003) no. 3, pp. 307-315. http://geodesic.mathdoc.fr/item/KYB_2003_39_3_a6/

[1] Chen, Ming-Hui, Shao,, Qi-Man, Ibrahim J. Q.: Monte Carlo Methods in Bayesian Computation. Springer, New York 2000 | MR | Zbl

[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 | Zbl

[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 | MR

[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 | Zbl

[7] Viallefont V., Richardson, S., Green P.: Bayesian analysis of Poisson mixtures. J. Nonparametric Statistics 14 (2002), 1-2, 181–202 | DOI | MR | Zbl