) with no extensions /1 28 (Due 5 Homework number

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7 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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)
with no extensions

/1
28
(Due

5
Homework number




1. Read Chapter 8.2.1 in Pearl's book. Answer Exercise 8.1a.



2
. Prove that if the
distribution

on the parameters (t
00
,t
01
,t
10
,t
11
)
of two binary
random
variables
(
X,Y
)

is distributed Dirichlet
(a
00
,a
01
,a
10
,a
11
)
, then

(
A
)
(
t
0

=
t
00
+t
01
,

t
1

= t
1
0
+t
11
)

is distributed Dirichlet.

(B) (t
0|
0

= t
00
/(t
00
+t
01
),

t
1|
0

= t
01
/(t
00
+t
01
)
) is distributed Dirichlet.

(C)
The

random variables (t
0
,

t
1
) in

(A) are independent of the random

variables
(t
0|
0
,

t
1|
0
) in (B).

(
D) Explain the meaning of this result for Bayesian learning of BNs.



3.
Search the literature for an

application of Bayesian networks/Markov
networks/HMMs in
the area

of
finance/economy/stock market
s
. Present a model;
discuss the feasibility of inference
and/or learning algorithms in the application you
chose.
Devote at least one page
for well

written and hopefully somewhat novel ideas.