3. Consider the following model Yilni N(Mi, 0%), Mi M + bis bi N(0,0z), i=1,...,n, j = 1, ..., Ni, independently; 2 = i=

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3 Consider The Following Model Yilni N Mi 0 Mi M Bis Bi N 0 0z I 1 N J 1 Ni Independently 2 I 1 (135.18 KiB) Viewed 13 times

3. Consider the following model Yilni N(Mi, 0%), Mi M + bis bi N(0,0z), i=1,...,n, j = 1, ..., Ni, independently; 2 = i= 1,...,n, independently; 2 y where ul, on, and oz are fixed constants. (a) Derive the joint probability density function of the {Hij} and the {b;} under the model pb, y). [3 MARKS] 7 • (b) Find the full conditional distributions of bị. These should be known distributions. [6 MARKS] (c) Explain how you can sample from p(by). [2 MARKS] (d) Suppose that a sample blt), t 1, ...,T, from the posterior distribution of b is available. Explain how you can use it to compute an estimate of the posterior predictive distribution of a future observation Ō. [3 MARKS] a