5. Assuming a linear model y = rB+ € where e is normally distributed as N(e|0, o2) and B with a normal prior distribution N(8|0, a2), (a) obtain the posterior N(8|3, 7?) where g2 r2 + o2 (b) Evaluate the integral below for a new observation {y0, xo} (y0|20, y) = | P(y0|ro, B, y)p(S\y)dß = | N(y0|r03, o2)N (B|3, y²)dß to show that the predictive posterior p(yolro, y) is another gaussian. Determine its mean and variance.
5. Assuming a linear model y = rB+ € where e is normally distributed as N(e|0, o2) and B with a normal prior distribution N(8|0, a2), (a) obtain the posterior N(8|3, 7?) where g2 r2 + o2 (b) Evaluate the integral below for a new observation {y0, xo} (y0|20, y) = | P(y0|ro, B, y)p(S\y)dß = | N(y0|r03, o2)N (B|3, y²)dß to show that the predictive posterior p(yolro, y) is another gaussian. Determine its mean and variance.
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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Transcribed Image Text:5. Assuming a linear model
y = rß+€
where e is normally distributed as N(e|0, o2) and B with a normal prior distribution N(B|0, a2),
(a) obtain the posterior N(8|3, 7?) where
r2 + o2
(b) Evaluate the integral below for a new observation {y0, xo}
p(y0|20, y) = | P(y0|ro, B, y)p(8\y)dB = | N(y0|r03, 0?)N (B|3, y²)dß
to show that the predictive posterior p(yolro, y) is another gaussian. Determine its mean
and variance.
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