README COPY OF Quiz 7 (Uncertainty Lectures 1- 5)
Due No due date Points 46 Questions 4 Available after Nov 27 at 2pm Time Limit None
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LATEST Attempt 1 20 minutes 0 out of 46 *
* Some questions not yet graded
Submitted Dec 2 at 3:39am
Question 1
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You test positive for disease D. The test T has a false positive rate of 3% (i.e., the probability of a positive test given that you do not have the disease, and a false negative rate of 3% (the probability of a negative test given that you do have the disease). In the general population 1 person out of 10,000 has disease D.
Give your answer rounded up to 3 significant digits. E.g., if the answer is 0.03456 you would enter 0.0346
What is the probability you have D given you test positive?
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.00322
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Question 2
0 / 3 pts
Repeat this previous question but when test T has false negative rate of 49%
.00170
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Consider the following Bayes Net
The variables A, B, C, and D have domains = {True, False} which we abbreviate as {t, f}, while variable E has domain {1, 2, 3}
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The CPTs for this network are as follows: P(A) =
A
P(A)
t
0.8
f
0.2
P(B|A) =
B
A
P(B|A)
t
f
0.2
f
f
0.8
t
t
0.8
f
t
0.2
P(C|A) =
C
A
P(C|A)
t
f
0.8
f
f
0.2
t
t
0.2
f
t
0.8
P(D|B,C) =
D
B
C
P(D|B,C)
t f f 0.1
t
f
f
0.1
f
f
f
0.9
t
f
t
0.5
f
f
t
0.5
t
t
f
0.5
f
t
f
0.5
t
t
t
0.9
f
t
P(E|D) =
t
0.1
E
D
P(E|D)
1
f
0.6
2
f
0.3
3
f
0.1
1
t
0.1
2
t
0.3
3
t
0.6
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Question 3
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In the Bayes net above we will use variable elimination (VE) to compute P(A|E=3) eliminating the variables in the order B, C, D.
Answer the following questions
1. For each factor in the sequence of factors that will be computed by VE as each variable is eliminated give the factor’s scope and size, where size is the number of entries in the factor. Use a table like the following to give your answer
Variable Eliminated
Scope of Factor computed by VE
size (number of entries in factor)
B
C
D
2. For each factor specify in a table its values. Use a table like the follow to specify each of the factors
in this example table, we are specifying a factor over the variables X, Y, Z by giving the values in the table.
3. Specify the final posterior probabilities, i.e., P(A=t|E=3) and P(A=f|E=3)
Your Answer:
X
Y
Z
F(X,Y,Z)
‘a’
‘a’
0
0.5
Part 1 (5 marks no part marks)
Eliminated Scope size
B A,C,D 8 C A,D 4 DA2
Part 2 (10 marks total)
Factor 1 (5 marks. 4 marks if <= 2 errors, 3 marks if <= 4 errors. An error is any of the entries in the row being wrong)
Note the columns and rows might be ordered differently, but for each specified assignment to A, D, C the value should be correct.
A D C F(A,D,C) ttt 0.82 ttf 0.42 tft 0.18 tff 0.58 ftt 0.58 ftf 0.18 fft 0.42 fff 0.82
Factor 2 (3 marks no part marks)
A D F(A,D)
t t 0.5
t f 0.5
f t 0.5
f f 0.5
Factor 3 (2 marks no part marks)
A F(A)
t 0.35
f 0.35
Part 3 (5 marks)
P(A=t|E=3) = 0.8, P(A=f|E=3) = 0.2
Question 4
Not yet graded / 20 pts
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In the Bayes net above use variable elimination (VE) to compute P(E|C=t) eliminating the variables in the order A, B, D.
Answer the following questions (specify all values with 3 significant digits)
1. For each factor computed by variable elimination specify in a table its values. Use a table like the follow to specify each of the factors
in this example table, we are specifying a factor over the variables X, Y, Z by giving the values in the table.
2. Specify the final posterior probabilities for P(E|C=t) Your Answer:
X
Y
Z
F(X,Y,Z)
'a'
'a'
0
0.5
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Part (15 marks total)
Note the columns and rows might be ordered differently, but for each specified assignment to B the value specified should be correct.
Factor 1 (5 marks no part marks) (eliminate A get factor over B since C is already removed as it is in evidence)
B F(B)
t 0.16
f 0.16
Factor 2 (5 marks no part marks) (eliminate B get factor over D)
D F(D)
t 0.224
f 0.096
Factor 3 (5 marks no part marks) (eliminate D get factor over E)
A F(E)
1 0.08
2 0.096
3 0.144
Part 2 (5 marks)
P(E=1|C=t) = 0.25 P(E=2|C=t) = 0.3 P(E=3|C=t) = 0.5