Statistical Evidence Evaluation, fall semester 2013
Solutions to Exercises 5
1. a) Network for evaluation at activity level.
Hp : ”The suspect was walking around close to the backdoor”
Hd : ”The suspect has never been in the neighbourhood of the backdoor”
Transfer and background depend on footwear type. Ambiguous
information in task. It is not about the soil type.
soiltransfer.txt
soilresidues.txt
Type
.
.
A
A
C
F
C
E
.
.
Type
.
.
F
D
E
D
D
A
.
.
Transfer?
NoTransfer
Transfer
NoTransfer
Transfer
Transfer
NoTransfer
Residues?
NoSoil
NoSoil
NoSoil
Soil
NoSoil
NoSoil
104
129
115
115
108
103
Pattern
Description of files:
soiltranfser.txt
Hence, Six states for footwear type,
two states for each of the transfer and
background node to be included.
soilresidues.txt
Note! If we only use these six states
for footwear type we have to assume
they are the only possible states (i.e.
one of them is treated as ”state other”.
Activity?
H:
Hp
(0.5)
Hd
(0.5)
Type?
Type:
Pr
Pr
A
A
B
B
C
C
D
D
E
E
F
F
Transfer?
Pr
H
Hp
Type
Hd
A
B
C
D
E
F
A BCDE F
Transfer
tA
tB
tC
tD
tE
tF
0 0 0 0 0 0
NoTransfer
1 - tA
1 - tB
1 - tC
1 - tD
1 - tE
1 - tF
1 1 1 1 1 1
T:
Soil Background?
Pr
Type
B:
A
B
C
D
E
F
Soil
bA
bB
bC
bD
bE
bF
NoSoil
1 - bA
1 – bB
1 – bC
1 – bD
1 – bE
1 - bF
Match?
Pr
T
B
E:
Transfer
NoTransfer
Soil
NoSoil
Soil
NoSoil
Match
0
1

0
NoMatch
0
0
1–
0
Two groups
1
0
0
0
No group
0
0
0
1
How to inform the probability tables?
•  is taken directly from the information provided, i.e. 8 % = 0.08
• The probabilities of the nodes Transfer? and Soil background?
may be informed by tabulating the variables in the files
soiltransfer.txt and soilresidues.txt, but we may also use the
learning algorithm for subsets of the network.
Open soiltransfer.txt in
GeNIe:
Since the node Type and the corresponding variable in soiltransfer.txt
has the same identifier (Identifier in GeNIe and variable name in the
file) they are automatically connected. What is left to match is node T
with variable Transfer?
Now, since we do not wish the other nodes to be affected, we must fix
them. Click on Fixed nodes…
Check the nodes in which
the probabilities shall be
fixed – B, E, H.
Check ”Randomize..” and let
”Confidence” be equal to 1.
Note that the conditional probabilities of transfer given state Hd of
node Activity? have also been learnt. These have to be restored to
the original zeros and ones.
We may ake analogous steps for learning the probabilities of node Soil
background? - now using file soilresidues.txt (variable Pattern? in
data file should of course not be used.)
However, the variable Type is part of both files. It would be good to let
the current estimated probabilities for that node serve as input for the
algorithm.
Hence, we need to do this in two steps:
(1) Update the probabilities in node Type
(2) Fix the probabilities from (1) when learning the probabilities in
node Soil background?
for instance…
Use the ”standard”
setup again
Now (eventually), it is time to evaluate the match
Instantiate Match in node
Match?
The Bayes factor (likelihood
ratio) is
B
0.9789
 46.4
0.0211
b) The X-Y-variant
Soil on ground
Pr
X:
e

not_e
1–
Soil on shoes
Pr
T
Transfer
B
X
Y:
Soil
NoTransfer
NoSoil
Soil
NoSoil
e
not_e
e
not_e
e
not_e
e
not_e
e
0
0
1
0


0
0
not_e
0
0
0
1
1–
1–
0
0
Two groups
1
1
0
0
0
0
0
0
No group
0
0
0
0
0
0
1
1
There are no ”immediate” consequences for the background node (the
way we have set up that node – only considering presence or absence of
soil).
c) The probability tables are not affected, but we’ll have to instantiate
node Type to state F.
0.9961
B
 255.4
0.0039
2 a) Source network
Hp : The suspects shoe(s) made the mark(s)
Hd : Some other (pair of) shoe(s) made the mark
Source?
H:
Pr
Hp
(0.5)
Hd
(0.5)
Pattern?
H
E:
Pr
Hp
Hd
113
(1)

Other
(0)
1–
Find  by tabulating variable Pattern in file soilresidues.txt
We have to assume that given Hp the pattern of the suspect’s
shoe(s)is certain to be recovered . Realistic?
 
26
 0.017
1500
B
0.9833
 58.9
0.0167
We need to assume that the pattern recovered is not influenced by
presence/absence of soil on the soles. Maybe a bit unrealistic.
Instantiating nodes Soil on shoes, Soil on ground and Pattern?
0.9996
B
 2499
0.0004
In addition, Instantiating nodes type to state F
0.99995
B
 19999
0.00005
3.
Instantiate the first states of both node Seat findings and node Pull-over
findings
The posterior probability that the suspect drove the escape car is 0.032
4.
a)