For iid Poisson variates y1,, yn with parameter ????, suppose ???? gamma(????, k) (Recall Section 4.7.2).
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For iid Poisson variates y1,…, yn with parameter ????, suppose ???? ∼ gamma(????, k) (Recall Section 4.7.2).
a. Show that the posterior distribution of ???? is gamma (i.e., the prior is conjugate), with posterior mean that is a weighted average of the sample mean and the prior mean. Explain how the weights change as n increases.
When n is very large, show that the posterior distribution has approximate mean ȳ and approximate variance ȳ∕n.
b. Find the posterior predictive distribution.
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Related Book For
Foundations Of Linear And Generalized Linear Models
ISBN: 9781118730034
1st Edition
Authors: Alan Agresti
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