Purpose
Apply inference to Bayesian Networks to reason about uncertainty. This technique is useful for real-world problems that can be modeled as an inference problems, such as for determining an insurance premium.
Objectives
Learners will be able to:
- Familiarize with the representation of Bayesian Networks.
- Apply inference techniques to Bayesian Network to reason about uncertainty.
- Solve complex inference problems with Bayesian Network.
Technology Requirements
NA
Assignment Description and Directions
It is in a parallel universe, the Good and the Evil are fighting for the earth. If the Good win, people are more likely to live a better life, but Evil can also make people’s life better (for their evil purpose). Knowing the probability, the analysts on the parallel universe model the situation with the Bayes Network as shown below:
Part 1
You will be calculating and typing in your numeric results to a specific place value. Refer to the assignment submission area in the course to input and submit your answers.
Figure 3.0: Bayesian Network
It is in a parallel universe, the Good and the Evil is fighting for the earth. If the Good win, people are more likely to live a better life, but Evil will also try to make people’s life better (for their evil purpose). Knowing the probability, the analysts on the parallel universe model the situation in Figure 3.0: Bayesian Network.
| G | B | P(G, B) |
| +g | +b | 1.a |
| +g | -b | 1.b |
| -g | +b | 1.c |
| -g | -b | 1.d |
Figure 3.1: Joint Probability Table
Review Figure 3.0: Bayesian Network and Figure 3.1: Joint Probability Table. What is the joint probability for 1.a, 1.b, 1.c, and 1.d?
Part 2
You will be calculating and typing in your numeric results to a specific place value. Refer to the assignment submission area in the course to input and submit your answers.
The winner of the fight claims that they are the Good, but we cannot be sure. What is the conditional probability P(+g|+b) that the Good won the fight knowing that people’s life is getting better?
Part 3
You will be calculating and typing in your numeric results to a specific place value. Refer to the assignment submission area in the course to input and submit your answers.
Figure 3.2
Review Figure 3.2. Now, assume we have observed more evidence, therefore we can make better inferences. The analysts on the parallel universe introduced two new random variables:
- Whether there are more kind people (K).
- Whether there are more greedy people (Y).
Table 3.3
Review Table 3.3, which shows the full joint distribution. What are the values of 3.a – 3.o?
Part 4
You will be calculating and typing in your numeric results to a specific place value. Refer to the assignment submission area in the course to input and submit your answers.
4.a Using either full joint distribution or conditional tables, what is the probability of P(+y|+g)? 4.b Using either full joint distribution or conditional tables, what is the probability of P(+y|+b,+g)?
4.c Using either full joint distribution or conditional tables, what is the probability of P(+y)?
4.d Using either full joint distribution or conditional tables, what is the probability of P(+k |+y)?
Submission Directions for Assignment Deliverables
Refer to the assignment submission space in the course to type and submit your answers. You will have one attempt to submit your answers. This assignment is auto-graded and feedback is provided.
This assignment submission is set as a Quiz type to enable auto-grading, with a duration of the quiz set as 3 hours. Since you would already know the questions from the PDF document, start the quiz/assignment only after you have completed it and are ready with the answers. Since the assignment is auto-graded and feedback is provided, strictly only one submission is allowed. Re-submission will not be allowed for any reason including errors that mistakenly occurred while entering the answers.
