Find a family of conjugate priors for the likelihood 1(|x) = p(x|a,), where p(x |a, ) is

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Find a family of conjugate priors for the likelihood 1(β|x) = p(x|a,β), where p(x |a, β) is as in the previous question, but a is known.

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Find a (two-dimensional) sufficient statistic for (a, β) given an n-sample x = (x₁, x₂,...,x_n) from the two-parameter gamma distribution

p(x|a, B) = {pr(a)}-xa- exp(-x/B) (0 < x < 0)

where the parameters a and β can take any values in 0 < a

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Bayesian Statistics An Introduction

ISBN: 9781118332573

4th Edition

Authors: Peter M. Lee

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Question Posted: Nov 28, 2023 04:23 AM

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Find a family of conjugate priors for the likelihood 1(|x) = p(x|a,), where p(x |a, ) is

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p(x|a, B) = {pºr(a)}-xa-¹ exp(-x/B) (0 < x < ∞0)

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For the given likelihood function 13x pxa where pxa is the two parameter gamma dis...View the full answer

Bayesian Statistics An Introduction

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