Perbandingan modél Bayes

modél data posterior probabiliti, P(H|D), ngagunakeun Bayes' theorem:

P(H|D) = P(D|H)P(H)/P(D)

Wates konci data-dependent P(D|H) nyaéta likelihood, jeung kadangkala disebut kajadian keur modél H; evaluasi nu bener mangrupa konci dina modél perbandingan Bayes.

Kajadian umumna normalizing constant atawa partition function tina kaputusan séjén, disebut modél paramater kaputusan H ti data D.

Hal nu asup akal di modél dua béda H1 jeung H2, parametrised ku modél vektor $\theta _{1}$ jeung $\theta _{2}$ nu ditaksir maké Bayes factor dirumuskeun ku

${\frac {P(D|H2)}{P(D|H1)}}={\frac {\int P(\theta _{2}|H2)P(D|\theta _{2},H2)\,d\theta _{2}}{\int P(\theta _{1}|H1)P(D|\theta _{1},H1)\,d\theta _{1}}}.$

Sumber sejen

• Gelman, A., Carlin, J.,Stern, H. and Rubin, D. Bayesian Data Analysis. Chapman and Hall/CRC.(1995)
• Bernardo, J., and Smith, A.F.M., Bayesian Théory. John Wiley. (1994)
• Lee, P.M. Bayesian Statistics. Arnold.(1989).
• Denison, D.G.T., Holmes, C.C., Mallick, B.K., Smith, A.F.M., Bayesian Methods for Nonlinéar Classification and Regression. John Wiley. (2002).
• Richard O. Duda, Peter E. Hart, David G. Stork (2000) Pattern classification (2nd edition), Section 9.6.5, p. 487-489, Wiley, ISBN 0471056693
• Chapter 24 in Probability Theory - The logic of science by E. T. Jaynes, 1994.
• David J.C. MacKay (2003) Information théory, inference and léarning algorithms, CUP, ISBN 0521642981, (also available online)

Tumbu kaluar

• The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, has many chapters on Bayesian methods, including introductory examples; compelling arguments in favour of Bayesian methods; state-of-the-art Monte Carlo methods, message-passing methods, and variational methods; and examples illustrating the intimate connections between Bayesian inference and data compression.

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