Consider the Bayesian linear model where The prior for is given by Yi ~ N(xi,...

Transcribed Image Text:

Consider the Bayesian linear model where The prior for ß is given by Yi ~ N(xiß, 0²), 72 n Σ=0, Σ = n i=1 i= 1, ... ,n, i=1 and 72 Σþriyi = Y. i=1 T(B) = 0.5 1(3 = 0) +0.5 N(3|0, 7²), where 1(3 = 0) is the probability mass function which puts all probability on 3 = 0. Suppose and 7 are known. (3) (12 pts) Hence, show that T(BY₁, •, Yn) x ..... and find vand . 7L IN(y₂ | 0,0²) 1(3 = 0) + m(y₁,..., Yn) N (B | v, ²) (0²2)} z=1 (4) (8 pts) Hence, write down (3 = 0 | y₁,..., yn). (5) (10 pts) What is the significance of the term m(y₁, ..., yn) II1N(yi | 0,0²) and show that this converges to infinity as y² grows. Consider the Bayesian linear model where The prior for ß is given by Yi ~ N(xiß, 0²), 72 n Σ=0, Σ = n i=1 i= 1, ... ,n, i=1 and 72 Σþriyi = Y. i=1 T(B) = 0.5 1(3 = 0) +0.5 N(3|0, 7²), where 1(3 = 0) is the probability mass function which puts all probability on 3 = 0. Suppose and 7 are known. (3) (12 pts) Hence, show that T(BY₁, •, Yn) x ..... and find vand . 7L IN(y₂ | 0,0²) 1(3 = 0) + m(y₁,..., Yn) N (B | v, ²) (0²2)} z=1 (4) (8 pts) Hence, write down (3 = 0 | y₁,..., yn). (5) (10 pts) What is the significance of the term m(y₁, ..., yn) II1N(yi | 0,0²) and show that this converges to infinity as y² grows.

Answer rating: 100% (QA)

Lets go through the given information and address the question step by step Given information 1 Baye... View the full answer