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Jeffreys' prior: For the multivariate normal model, Jeffreys' rule for gen- erating a prior distribution on (0, 2) gives pJ(0, E) x |Σ(p+2)/2 a) Explain why the function pj cannot actually be a probability density for (0, E). b) Let pj(0, y₁,..., yn) be the probability density that is proportional to py(θ, Σ)xp(31,...,3η θ, Σ). Obtain the form of pJ(θ,Σ|11,...,Ψη), Pj0E.y₁..... yn) and p₁y₁..... Yn).

Jeffreys' prior: For the multivariate normal model, Jeffreys' rule for gen- erating a prior distribution on (0, 2) gives pJ(0, E) x |Σ(p+2)/2 a) Explain why the function pj cannot actually be a probability density for (0, E). b) Let pj(0, y₁,..., yn) be the probability density that is proportional to py(θ, Σ)xp(31,...,3η θ, Σ). Obtain the form of pJ(θ,Σ|11,...,Ψη), Pj0E.y₁..... yn) and p₁y₁..... Yn).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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7.1 Jeffreys' prior: For the multivariate normal model, Jeffreys' rule for gen- erating a prior distribution on (0, 2) gives pJ(0, ) x (p+2)/2 a) Explain why the function pj cannot actually be a probability density for (0, E). b) Let pj(0, y₁,..., yn) be the probability density that is proportional to pj(0, E)xp(y₁,..., yn 0, E). Obtain the form of pj(0, y₁,..., yn), Yn py(0|2,31,..., PJ (0, y₁,..., yn) and ps(y₁,..., yn).
Transcribed Image Text:7.1 Jeffreys' prior: For the multivariate normal model, Jeffreys' rule for gen- erating a prior distribution on (0, 2) gives pJ(0, ) x (p+2)/2 a) Explain why the function pj cannot actually be a probability density for (0, E). b) Let pj(0, y₁,..., yn) be the probability density that is proportional to pj(0, E)xp(y₁,..., yn 0, E). Obtain the form of pj(0, y₁,..., yn), Yn py(0|2,31,..., PJ (0, y₁,..., yn) and ps(y₁,..., yn).
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