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手写代写-ECS773P

时间：2021-05-06

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

all instructions on the download page.

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

that you check your submission before uploading it. Calculators are permitted in this

examination.

Answer ALL questions. You MUST adhere to the word limits, where

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

学霸联盟

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

all instructions on the download page.

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

that you check your submission before uploading it. Calculators are permitted in this

examination.

Answer ALL questions. You MUST adhere to the word limits, where

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

学霸联盟