2. Let ¥ = {0,1} and A= {0,1,¢}. This models an erasure option, ic. a method of saying “I don’t knowwhat the state is”. Suppose that the observation distributions are Gaussian with mean depending...

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2. Let ¥ = {0,1} and A= {0,1,¢}. This models an erasure option, ic. a method of saying “I don’t know what the state is”. Suppose that the observation distributions are Gaussian with mean depending on the state: Py = N(—1,07) and P; = N (1,07). Suppose that the cost has the following structure, parameterized by 0 < e:="" c(0,0)="" c(0,1)="" c(o,e)\="" fo="" 1="" e="" ce,0)="" c,1)="" cu,e)/="" ~\1="" 0="" ce)”="" assume="" that="" the="" prior="" is="" symmetric:="" (0)="a(1)" =="" 1/2.="" (a)="" show="" that="" if="" ¢="">< 1/2,="" the="" bayes="" rule="" has="" the="" form="" 0=""><-t ony)="Ve"><> 1/2.

problem2-1b0jja15.pdf

Answered Same DaySep 08, 2022

Answer To: 2. Let ¥ = {0,1} and A= {0,1,¢}. This models an erasure option, ic. a method of saying “I don’t...

Banasree answered on Sep 08 2022

76 Votes

2 a.
We know that any unique Bayes estimator is admissible.
For y, t risk rule is yX+t
R(e , yX+t) = Y^2σ^2 + [(y-1)c+t]^2
a) c<1/2
the (y-1)^>1 and
p(y,t) >= [(y+1)e + t)^2
= (y-1)^2[e+(t/(y-1))^2
· {e+(t/(y-1)}^2
· p(0, -t/(y-1)
·
b)If c> = ½
P(1/2, t) = σ^2+t^2> σ^2 =...

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2. Let ¥ = {0,1} and A= {0,1,¢}. This models an erasure option, ic. a method of saying “I don’t knowwhat the state is”. Suppose that the observation distributions are Gaussian with mean depending...

Answer To: 2. Let ¥ = {0,1} and A= {0,1,¢}. This models an erasure option, ic. a method of saying “I don’t...

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