Reference no: EM132376391

Risk Modelling Assignment Sheet

Use those knowledge section to complete the assignament

- Basic Byesian Network
- Beyesian network structure (
- Probabilities for Discrete Nodes ( Labelled node, Boolean nodes, And, OR function, noisyand, noisyor function, ranked node, Naive BNs
- Probabilities for Continuous Nodes
- Testing Bayesian Networks

1. Horse Race

Let's assume that there is a race between two horses: Fleetfoot and Dogmeat, and you want to determine which horse to bet on. Fleetfoot and Dogmeat have raced against each other on twelve previous occasions, all two-horse races. Of these last twelve races, Dogmeat won five and Fleetfoot won the other seven. Therefore, all other things being equal, the probability of Dogmeat winning the next race can be estimated as 5/12 or 0.417 or 41.7%. However, on three of Dogmeat's previous five wins, it had rained before the race. It had rained only once on any of the days that he lost. On the day of the race in question, it is raining.

Construct a Bayesian network to show the probability of Dogmeat winning the race. Explain your Bayesian network and how you obtained your answer.

2. Disease Test

Consider the example of a test to determine if a person has a particular disease. First construct the following Bayesian network (Figure 2.1) to predict the probability of a person having the disease if they return a positive test result. 1 in 1000 people within the population have the disease (Table 2.1). If a person has the disease then there is a 100% chance that the test will be positive and if the person does not have the disease then there is a 5% chance that the test will be positive (Table 2.2).

3. Flower Breeding

You are a flower breeder. The plant you are breeding can either have red flowers or white flowers. You know that the colour of a flower depends on the genotype of the plant. The gene for red flowers (represented by R) is a dominant gene and the gene for white flowers (represented by r) in a recessive gene. Therefore, a plant with the genotype RR or Rr has red flowers, while a plant with the genotype rr has white flowers. Hence, the colour of a plant's flowers is influenced by its genotype (as shown in Figure 3.1) and the probability of a plant having red or white flowers, given its genotype, is shown in Table 3.1.

Construct a Bayesian Network and use it to determine the probability that the second generation offspring will have red flowers? Explain your Bayesian network and how you obtained your answer.

4. Horse Stud

You are the manager of a horse stud. A colt called John has been found to suffer from a life-threatening hereditary disease caused by a recessive gene. The disease is so serious that John's parents, Henry and Irene, are taken out of the stud-breeding program. However, you still need to decide which of the remaining horses in the stud are likely to carry the disease-causing gene and therefore should be removed from the breeding program. You look through the stud records to retrace John's family tree (Table 4.1).

Construct a Bayesian Network to help you determine which horses in the stud are most likely to be carriers of the disease-causing gene and should be culled from the breeding program. You have one further piece of information to assist your decision - Fred has previously been tested for the disease-causing gene and he is not a carrier (he is pure). Which horse(s) will you cull from the breeding program? Explain your Bayesian network and how you obtained your answer.

5. Military Craft

You have been employed by the military to develop a system for identifying enemy military craft based on the type of signal they emit and where the signal is detected.

Construct a Bayesian network that will help you to predict the most likely enemy craft depending on where it is detected (land, sea or air) and the type of signal that it is using (radio type A, radio type B, radar type X and radar type Y).
If you detect an enemy craft signal over land and the signal is radar type X, what would be the most likely type of craft?
If you detect an enemy craft signal over sea and the signal is radar type X, what would be the most likely type of craft?
If you detect an enemy craft signal over air and the signal is radar type X, what would be the most likely type of craft?

You have the following information to help you construct your Bayesian network:

Enemy craft can be land, sea or air craft. You know that 80% of the time land craft will be detected on land, 80% of the time sea craft will be detected on sea and 80% of the time air craft will be detected in the air (Table 5.1). Therefore the general type of craft determines the sensed location of the craft.

Attachment:- Risk Modelling Assignment Sheet.rar