Hierarchical Model: Definition
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Nonconjugate hierarchical models: suppose that in the rat tumor example, we wish to use a normal population distribution on the log-odds scale: logit(θj) ∼N(μ, τ^2), for j=1, …, J. As in Section 5.3, you will assign a noninformative prior distribution to the hyperparameters and perform a full Bayesian analysis. (a) Write the joint posterior density, p(θ, μ, τ|y). (b) Show that the integral (5.4) has no closed-form expression. (c) Why is expression (5.5) no help for this problern? In practice, we
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