A characterization of the bivariate wishart distribution

• Autorzy: Geiger D. , Heckerman D.
• Języki publikacji: EN

Abstrakty

EN

We provide a characterization of the bivariate Wishart and normal-Wishart distributions. Assume that x = {x₁,x<sub.2</sub>} has a non-singular bivariate normal pdf f(x) = N (μ, W) with unknown mean vector fi and unknown precision matrix W. Let f(x)= f(x₁)f(x₂|x<sub.1</sub>), where f(x₁) = N{m₁ 1/ν₁ and f(x₂ | x₁) = N{m_2|1 + b₁₂x₁ l/ν_2|1). Similarly, define {ν₂, b₂₁,m₂, m_1|2} using the factorization f(x)=f(x₂)f(x₁|x₂)- Assume μ and W have a strictly positive joint pdf f_μw(μW). Then f_μw is a normal-Wishart pdf if and only if global independence holds, namely,…[formula] and local independence holds, namely, [formula] (where x* denotes the standardized r.v. x and stands for independence). We also characterize the bivariate pdfs that satisfy global independence alone. Such pdfs are termed hyper-Markov laws and they are used for a decomposable prior-to-posterior analysis of Bayesian networks.

Słowa kluczowe

EN

bivariate Wishart; bivrariate equation; Bayesian networks

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1998
• Tom: Vol. 18, Fasc. 1
• Strony: 119--131
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Geiger D.

• Computer Science Department, Technion, Haifa 32000, Israel

autor

Heckerman D.

• Microsoft Research, Bldg 9S, Redmond WA, 98052-6399, U.S.A.

Bibliografia

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