3 Bayesian Regression.pdf revised edition_2021

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yesian Regression Analysis (see exercises) IV-2 4.1. Introduction • Classical regression model y X= + β ε • y is an Nx1 vector of observations • X is an Nxd matrix of known coefficient... s • β is a dx1 vector of parameters • ε is an Nx1 vector of random errors • Assumption: ( ) 2 N , 0 σ ΙN ε ∼ ⇒ Normal linear model ( ) 2 y X ∼ N , β σ ΙN , with likelihood ( ) ( ) { ( )( ) ( )} N 2 T 22 2 f , , 2 exp 2 − yX y X y X β ββ σ πσ − − − σ ∼ (1) • β = − X X Xy T d i 1 is the classical MLE / LSE • S T =− − yX yX e je j β β is the RSS & s N d S 2 1 = − • All models are conditional on X ⇒ Omit X in notation ⇒ f cy X,, ² β σ g becomes f ,² ( ) y β σ IV-3 4.2. An example: the life [Show More]

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