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Osoba O, Mitaim S, Kosko B. Bayesian inference with adaptive fuzzy priors and likelihoods. IEEE Trans Syst Man Cybern B Cybern. 2011;41(5):1183-97doi: 10.1109/TSMCB.2011.2114879.
Osoba, O., Mitaim, S., & Kosko, B. (2011). Bayesian inference with adaptive fuzzy priors and likelihoods. IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society, 41(5), 1183-97. https://doi.org/10.1109/TSMCB.2011.2114879
Osoba, Osonde, et al. "Bayesian inference with adaptive fuzzy priors and likelihoods." IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society vol. 41,5 (2011): 1183-97. doi: https://doi.org/10.1109/TSMCB.2011.2114879
Osoba O, Mitaim S, Kosko B. Bayesian inference with adaptive fuzzy priors and likelihoods. IEEE Trans Syst Man Cybern B Cybern. 2011 Oct;41(5):1183-97. doi: 10.1109/TSMCB.2011.2114879. Epub 2011 Apr 07. PMID: 21478078.
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IEEE Trans Syst Man Cybern B Cybern. 2011 Oct;41(5):1183-97. doi: 10.1109/TSMCB.2011.2114879. Epub 2011 Apr 07.

Bayesian inference with adaptive fuzzy priors and likelihoods.

IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society

Osonde Osoba, Sanya Mitaim, Bart Kosko

Affiliations

  1. Department of Electrical Engineering, Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089-2564, USA.

PMID: 21478078 DOI: 10.1109/TSMCB.2011.2114879

Abstract

Fuzzy rule-based systems can approximate prior and likelihood probabilities in Bayesian inference and thereby approximate posterior probabilities. This fuzzy approximation technique allows users to apply a much wider and more flexible range of prior and likelihood probability density functions than found in most Bayesian inference schemes. The technique does not restrict the user to the few known closed-form conjugacy relations between the prior and likelihood. It allows the user in many cases to describe the densities with words and just two rules can absorb any bounded closed-form probability density directly into the rulebase. Learning algorithms can tune the expert rules as well as grow them from sample data. The learning laws and fuzzy approximators have a tractable form because of the convex-sum structure of additive fuzzy systems. This convex-sum structure carries over to the fuzzy posterior approximator. We prove a uniform approximation theorem for Bayesian posteriors: An additive fuzzy posterior uniformly approximates the posterior probability density if the prior or likelihood densities are continuous and bounded and if separate additive fuzzy systems approximate the prior and likelihood densities. Simulations demonstrate this fuzzy approximation of priors and posteriors for the three most common conjugate priors (as when a beta prior combines with a binomial likelihood to give a beta posterior). Adaptive fuzzy systems can also approximate non-conjugate priors and likelihoods as well as approximate hyperpriors in hierarchical Bayesian inference. The number of fuzzy rules can grow exponentially in iterative Bayesian inference if the previous posterior approximator becomes the new prior approximator.

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