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CSCI 573 2010 Homework Assignment 2
Due:
March 2nd, 2010 before the class 12:30pm
(either in person or electronically)
1 Parameter Learning
Q
H
int. You can get some intuition by looking at Exercise 17.1 which is a
special case of this problem. )
Q
2 (7 pts) In class when we discussed Bayesian parameter learning, we have used the Beta prior for the
coin/thumbtack tossing example. Now, let us try a diﬀerent prior for thumbtacks. Let
θ
be the probability
of thumbtack being “up”. Our prior takes the form
p
(
θ
) =
±
2
θ
if
θ
≤
1
/
2
2(1

θ
) if 1
/
2
≤
θ
≤
1
We now see one observation that the thumbtack is in “up” position after tossing. Answer following: i) what
is the posterior distribution of
θ
? ii) what is the MAP estimate of
θ
?
Q
comment on why the equation in (b) is an approximation. Particularly, since data are assumed to be inde
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