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Q1 (a) Let X1,..., Xn be iid obser vations from an exponential(A) pdf, where A has the conjugate IG(a, b) prior, an inverted gamma with pdf a+1 ()**e-1/), 0 < A < oo. 1 r(a)ba Show how to find a 1- a Bayes HPD credible set for A. (b) Find a 1- a Bayes HPD credible set for o, the variance of a normal distribu- tion, based on the sample variance s and using a conjugate IG(a, b) prior for (c) Starting with the interval from part (b), find the limiting 1-a Bayes HPD credible set for o obtained as a 0 and b 0o. 30-

Q1 (a) Let X1,..., Xn be iid obser vations from an exponential(A) pdf, where A has the conjugate IG(a, b) prior, an inverted gamma with pdf a+1 ()**e-1/), 0 < A < oo. 1 r(a)ba Show how to find a 1- a Bayes HPD credible set for A. (b) Find a 1- a Bayes HPD credible set for o, the variance of a normal distribu- tion, based on the sample variance s and using a conjugate IG(a, b) prior for (c) Starting with the interval from part (b), find the limiting 1-a Bayes HPD credible set for o obtained as a 0 and b 0o. 30-

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2- Answer the following question. Q1 (a) Let X1,..., Xn be iid obser vations from an exponential(A) pdf, where A has the conjugate IG(a, b) prior, an inverted gamma with pdf a+1 slqmsx 끼(시a, 6) = Tajb ) e-/6A), 0< ^ < o∞.AN Show how to find a 1- a Bayes HPD credible set for A. (b) Find a 1- a Bayes HPD credible set for o, the variance of a normal distribu- tion, based on the sample variance s and using a conjugate IG(a, b) prior for (c) Starting with the interval from part (b), find the limiting 1-a Bayes HPD credible set for o obtained as a 0 and b - 0o. 30-
Transcribed Image Text:2- Answer the following question. Q1 (a) Let X1,..., Xn be iid obser vations from an exponential(A) pdf, where A has the conjugate IG(a, b) prior, an inverted gamma with pdf a+1 slqmsx 끼(시a, 6) = Tajb ) e-/6A), 0< ^ < o∞.AN Show how to find a 1- a Bayes HPD credible set for A. (b) Find a 1- a Bayes HPD credible set for o, the variance of a normal distribu- tion, based on the sample variance s and using a conjugate IG(a, b) prior for (c) Starting with the interval from part (b), find the limiting 1-a Bayes HPD credible set for o obtained as a 0 and b - 0o. 30-
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