In Example 12.5.6, we used a hierarchical model. In that model, the parameters 1, . . .
Question:
a. Write the product of the likelihood and the prior as a function of the parameters μ1, . . . , μp, τ1, . . . , τp, ψ, and λ.
b. Find the conditional distributions of each parameter given all of the others. Hint: For all the parameters besides λ, the distributions should be almost identical to those given in Example 12.5.6. Wherever λ0 appears, of course, something will have to change.
c. Use a prior distribution in which α0 = 1, β0 = 0.1, u0 = 0.001, γ0 = δ0 = 1, and ψ0 = 170. Fit the model to the hot dog calorie data from Example 11.6.2. Compute the posterior means of the four μi’s and 1/τi’s. Distribution
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Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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