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fa(^; a, ß) = r(x) where a and ß are parameters of the distribution, and r(·) is the Gamma function (see Lecture 1 if don't remember what this function is), with derivative denoted by r'(-). Show that it is a conjugate prior of Poisson (A), i.e., when the observations X; for 1

fa(^; a, ß) = r(x) where a and ß are parameters of the distribution, and r(·) is the Gamma function (see Lecture 1 if don't remember what this function is), with derivative denoted by r'(-). Show that it is a conjugate prior of Poisson (A), i.e., when the observations X; for 1

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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May I know how to prove that the posterior distribution also follows Gamma distribution and so, what's the parameter? Thank you.

Question 7 The Gamma distribution Gamma(a, B) is given by -BA fa(^; a, B) T(x) where a and ß are parameters of the distribution, and r(-) is the Gamma function (see Lecture 1 if you don't remember what this function is), with derivative denoted by T'(-). Show that it is a conjugate prior of Poisson (A), i.e., when the observations X; for 1<i<n are independent identically distributed random variables with PDF equal to e¬^^xi fx; (xi) Xị! the posterior distribution also follows a Gamma distribution. What are its parameters?
Transcribed Image Text:Question 7 The Gamma distribution Gamma(a, B) is given by -BA fa(^; a, B) T(x) where a and ß are parameters of the distribution, and r(-) is the Gamma function (see Lecture 1 if you don't remember what this function is), with derivative denoted by T'(-). Show that it is a conjugate prior of Poisson (A), i.e., when the observations X; for 1<i<n are independent identically distributed random variables with PDF equal to e¬^^xi fx; (xi) Xị! the posterior distribution also follows a Gamma distribution. What are its parameters?
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