Statistics > Study Notes > 7 Gibbs Sampler General Idea DUKE UNIVERSITY (All)
7 Gibbs Sampler General Idea DUKE UNIVERSITY
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We have seen that Monte Carlo sampling is a useful tool for sampling from prior and posterior distributions By limiting attention to conjugate prior distributions, all models have had tractable pos... terior distributions so sampling was not really necessary (although convenient) What if we want to use a non-conjugate prior distribution? What if we cannot sample from the joint posterior distribution? Introduction to Gibbs Sampling – p. 1/12 Semi-Conjugate Examples Normal sampling model Yi | µ, φ iid∼ N (µ, 1 φ ) But now assume that µ is independent of φ a priori: µ ∼ N ( µ 0, 1/ω 0 ) φ ∼ G ( ν 0 / 2, ν0 σ 2 0 /2) Note: Hoff uses τ 2 0 in the variance for µ. I use ω 0 = 1/τ 2 0 , but results are identical. Introduction to Gibbs Sampling – p. 2/12 Posterior Distrib [Show More]
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