×

zbMATH — the first resource for mathematics

Gibbs sampling in Bayesian networks. (English) Zbl 0717.68086
Summary: Posterior probabilities in Bayesian networks can be evaluated by stochastic simulation. It is shown that the stochastic simulation can be viewed as a sampling from the Gibbs distribution. This view is useful in (1) making statements about convergence of the simulation and J. Besag ‘J. Roy. Statist. Soc., Ser. B 36, 192-236 (1974; Zbl 0327.60067)] finding the most likely instantiation of the Bayesian network.

MSC:
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
68U20 Simulation (MSC2010)
PDF BibTeX Cite
Full Text: DOI
References:
[1] Ackley, D.H.; Hinton, G.E.; Sejnowski, T.J., A learning algorithm for Boltzmann machines, Cognitive sci., 9, 147-169, (1985)
[2] Besag, J., Spatial interaction and the statistical analysis of lattice systems (with discussion), J. roy. stat. soc., B36, 192-326, (1974) · Zbl 0327.60067
[3] Cheeseman, P., A method of computing generalized Bayesian probability values for expert systems, (), 198-202
[4] Geffner, H.; Pearl, J., On the probabilistic semantics of connectionist networks, (), 187-195
[5] Geman, S., Stochastic relaxation methods for image restoration and expert systems, (), 265-311, also in
[6] Geman, S.; Geman, D., Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE trans. pattern anal. Mach. intell., 6, 6, 721-742, (1984) · Zbl 0573.62030
[7] Hinton, G.E.; Sejnowski, T.J., Learning and relearning in Boltzmann machines, (), 282-317
[8] Hrycej, T., Gibbs sampling, Bayesian networks and Boltzmann machines, ()
[9] Kim, J.H.; Pearl, J., A computational model for causal and diagnostic reasoning in inference systems, (), 190-193
[10] Pearl, J., On evidential reasoning in a hierarchy of hypotheses, Artif. intell., 28, 9-15, (1986)
[11] Pearl, J., Fusion, propagation and structuring in belief networks, Artif. intell., 29, 241-288, (1986) · Zbl 0624.68081
[12] Pearl, J., A constraint-propagation approach to probabilistic reasoning, (), 357-369
[13] Pearl, J., Evidential reasoning using stochastic simulation of causal models, Artif. intell., 32, 245-257, (1987) · Zbl 0642.68177
[14] Pearl, J., ()
[15] Pearl, J.; Verma, T., The logic of representing dependencies by directed graphs, (), 374-379
[16] Shastri, L.; Feldman, J.A., Evidential reasoning in semantic networks: A formal theory, (), 465-474
[17] Spiegelhalter, D.J., Probabilistic reasoning in predictive expert systems, (), 47-67
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.