Summer Examination Period 2021 – May/June – Semester B
ECS773P Bayesian Risk and Decision Analysis Duration: 3 hours
This is a 3-hour online exam, which must be started within a 24-hour period.
You MUST submit your answers within 3 hours of the time that you started the exam. Follow
You must upload a SINGLE PDF file containing your solutions. These can be typed or
handwritten, or a combination of the two. Multiple submissions are not permitted, so be sure
examination.
specified in the questions. Failure to do so will lead to those answers not being
marked.
YOU MUST COMPLETE THE EXAM ON YOUR OWN, WITHOUT CONSULTING OTHERS
Examiners: Professor Martin Neil and Dr Huy Phan
© Queen Mary University of London, 2021
Page 2 ECS773P (2021)
Question 1
A business software system is required to achieve at most 1 failure in 1000 demands (this is
equivalent to a probability of failure on demand: = 10−3). The business manager wants
to evaluate the system before delivery using a combination of expert judgment about the
process applied in its development and failure data collected during testing.
From an analysis of the development process applied the business manager believes that there
is a 70% chance that the system will meet the requirement and a 30% chance it is an order of
magnitude worse than that ( = 10−2). If the can take two values only, this is
expressed as the prior:
( = 10−3) = 0.7
( = 10−2) = 0.3
The testing process is assumed to comprise of a sequence of independent test demands, each
of which can result in failure or success.
The likelihood of observing failures in test demands is defined by the binomial
distribution conditioned on the number of demands, d, and the . Thus:
(|, ) =
!
! ( − )!
()(1 − )(−)
The posterior distribution for , using Bayes theorem, is:
(|, ) =
(|, )()
()
a) State the formula needed to calculate the marginal probability of ().
[5 marks]
b) During 200 test demands zero failures were discovered. What is the posterior probability
that the software meets the business requirement?
[20 marks]
[Question 1 TOTAL: 25 marks]
Page 3 ECS773P (2021)
Question 2
a) Produce two drawings illustrating the salient features of James Reason’s Swiss Cheese
model for rare catastrophic events. The first should show a situation where an accident is
prevented and the second where it is not.
[6 marks]
b) Define and then identify in your drawings the following salient features:
[8 marks]
Hazard
Failure
Vulnerability
Accident
c) For the event tree, shown in Figure 1, for a gas release accident, draw an equivalent
Bayesian network (BN) graph.
[8 marks]
Figure 1: Event tree for gas release accident
d) Comment on the difficulties encountered when attempting to determine the states for the
nodes in the BN model of c) and the values for the node probability tables.
[3 marks]
[Question 2 TOTAL: 25 marks]
Page 4 ECS773P (2021)
Question 3
a) For each of the three Bayesian network models shown in Figure 2, involving six variables
, , , , , , write the expression for the full simplified joint probability distribution
(, , , , , ).
[6 marks]
(i) (ii) (iii)
Figure 2 Bayesian network models for (,, ,, , )
b) Derive then draw the junction tree for each of the three Bayesian network models in
Question 2 a) above. [12 marks]
c) As accounts manager in your company, you classify 75% of your customers as a ‘good’
credit risk and the rest as ‘risky’ credit, depending on their credit rating. Customers in the
‘risky’ category allow their accounts to go overdue 50% of the time, whereas those in the
‘good’ category allow their accounts to become overdue only 10% of the time. What percentage
of overdue accounts are held by customers that are ‘risky’? [7 marks]
[Question 3 TOTAL: 25 marks]
End of Paper