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Q1 (a) Let X1,...,Xn be iid observations from an exponential(X) pdf, where A has th conjugate IG(a, b) prior, an inverted gamma with pdf 1 a+1 A"e-1/(b), 0

Q1 (a) Let X1,...,Xn be iid observations from an exponential(X) pdf, where A has th conjugate IG(a, b) prior, an inverted gamma with pdf 1 a+1 A"e-1/(b), 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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 1 a+1 slamsla, 6) = FYe )e-1/0»), 0<a < oo. W %3D Show how to find a 1- a Bayes HPD credible set for X. (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- Dr. Asieh Abtahi- Faculty of Mathematics and Statistics- Islamic Azad University of Shiraz - Iran 4
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 1 a+1 slamsla, 6) = FYe )e-1/0»), 0<a < oo. W %3D Show how to find a 1- a Bayes HPD credible set for X. (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- Dr. Asieh Abtahi- Faculty of Mathematics and Statistics- Islamic Azad University of Shiraz - Iran 4
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