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3. Consider the normal linear regression model y = r3+€ where e is normally distributed as N(e0, o²I,) and 3 with a prior distribution N(30, A) and o? with a prior distribution of IG(o (a,b). (a) Determine the posterior density p(3, oly) which is not a standard distribution. (b) Knowing the full conditionals, p(3ly, o2) (Normal) and p(a13, u) (Inverse Gamma); sample p(3, oly) using Gibbs method for the values of r 1, y = 0.4, a = 4, 6 = 2, n = 1 and A = 0.1 generate 30000 points for (3, o2) pair and compare their 2-D histogram with the analytical plot of p(3,0 ly) to check for their similarity.

3. Consider the normal linear regression model y = r3+€ where e is normally distributed as N(e0, o²I,) and 3 with a prior distribution N(30, A) and o? with a prior distribution of IG(o (a,b). (a) Determine the posterior density p(3, oly) which is not a standard distribution. (b) Knowing the full conditionals, p(3ly, o2) (Normal) and p(a13, u) (Inverse Gamma); sample p(3, oly) using Gibbs method for the values of r 1, y = 0.4, a = 4, 6 = 2, n = 1 and A = 0.1 generate 30000 points for (3, o2) pair and compare their 2-D histogram with the analytical plot of p(3,0 ly) to check for their similarity.

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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3. Consider the normal linear regression model y = r3+e where e is normally distributed as N(e0, o²I) and 3 with a prior distribution N(30, A) and o? with a prior distribution of IG(o (a,b). (a) Determine the posterior density p(3, 0ly) which is not a standard distribution. (b) Knowing the full conditionals, p(3ly, o2) (Normal) and p(a13, u) (Inverse Gamma); sample p(3, oly) using Gibbs method for the values of z 1, y = 0.4, a = 4, 6 = 2, n = 1 and A = 0.1 generate 30000 points for (3, a2) pair and compare their 2-D histogram with the analytical plot of p(3,0 ly) to check for their similarity.
Transcribed Image Text:3. Consider the normal linear regression model y = r3+e where e is normally distributed as N(e0, o²I) and 3 with a prior distribution N(30, A) and o? with a prior distribution of IG(o (a,b). (a) Determine the posterior density p(3, 0ly) which is not a standard distribution. (b) Knowing the full conditionals, p(3ly, o2) (Normal) and p(a13, u) (Inverse Gamma); sample p(3, oly) using Gibbs method for the values of z 1, y = 0.4, a = 4, 6 = 2, n = 1 and A = 0.1 generate 30000 points for (3, a2) pair and compare their 2-D histogram with the analytical plot of p(3,0 ly) to check for their similarity.
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