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

Question

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 y<-t
Ony)= Ve -tl tand find an expression for ¢ in terms of the parameters of the problem
(b) Find 6g when c¢ > 1/2.

problem2-1b0jja15.pdf

Banasree · Accepted Answer

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) c1 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 = p(1/2,

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...

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