a Let X1, ,Xn be iid observations from an exponential ( Icirc raquo ) pdf, where Icirc raquo has the conjugate IG(a, b) prior, an inverted gamma with pdf Show how to find a 1 Icirc plusmn Bayes HPD credible set for Icirc raquo b Find a 1 Icirc plusmn Bayes HPD credible set for Iuml 2, the variance of a normal distribution, based on the sample variance s2 and using a conjugate IG(a, b) prior for Iuml 2 c Starting with the interval from part (b), find the limiting 1 Icirc plusmn Bayes HPD credible set for Iuml 2 obtained as a 0 and b 1 (1 1 A) 0

Question: a. Let X1,... ,Xn be iid observations from an exponential (Î») pdf, where Î» has the conjugate IG(a, b) prior, an inverted gamma with pdf

a. Let X1,... ,Xn be iid observations from an exponential (Î») pdf, where Î» has the conjugate IG(a, b) prior, an inverted gamma with pdf

Show how to find a 1 - Î± Bayes HPD credible set for Î».
b. Find a 1 - Î± Bayes HPD credible set for Ïƒ2, the variance of a normal distribution, based on the sample variance s2 and using a conjugate IG(a, b) prior for Ïƒ2.
c. Starting with the interval from part (b), find the limiting 1- Î± Bayes HPD credible set for Ïƒ2 obtained as a †’ 0 and b †’ ˆž.

1 (1+-1/A) 0

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