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Question 4: Bayesian Belief Networks

[16]

The Durban Botanic Garden has an automatic lawn sprinkler system with sensors

that detect cloudy skies, and attempts not to water the lawn on rainy days. The

system and sensors are not completely accurate. Consider the following data about

weather

patterns in Durban, and the lawn

sprinkler

system of the Durban Botanic

Gardens:

1 out of every 2 days the sensors indicate

not-Cloudy

The rest of the time it indicates

Cloudy

It rains on 4 out of every 5 days that the sensors detect

Cloudy

skies.

It also rains on 1 out of every 5 days that the sensors detect

not-Cloudy

skies.

When the sensors indicate

Cloudy

skies, the sprinklers are set to run 10% of

the time.

When the sensors indicate

not-Cloudy

skies, the sprinklers run half the time.

The lawns can be

wet

from either rain, or the sprinklers that ran, or both. The

Garden wants to host a concert, and they want to use a Bayesian Belief Network to

determine if the lawn will be wet on that particular day, given that the sky is

Cloudy

or not.

(a)

Define the variables needed to construct a Bayesian Belief Network for the

given data. Define the domain for each variable. (4)

(b)

Calculate the conditional probability tables for the given data, using the vari-

ables you defined in (a). (6)

(c)

Draw the Bayesian Belief Network for this data. Show all the nodes and their

dependencies. (4)

(d)

Can we use this Bayesian Belief Network to answer the Durban Botanic

Gardens question? Why or why not?