Part 1: Application of Bayesian Networks
You are given the following description of a new transmissible disease COVID-22 and its available tests.
There are two tests for COVID-22 available: at-home rapid antigen test and PCR test. The first one can be taken at home and it takes around 30 mins to get a result while the PCR test needs to be carried out at a lab
The sensitivity and specificity of the at-home antigen test are 82% and 98% respectively.
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PC test on the other hand is more accurate than the rapid test. It is sometimes prescribed as a second confirmation test. PCR test accuracy is affected by how the sample is collected. If the sample is collected by
trained clinical staff, the sensitivity and specificity are 99.2% and 99.9%. On the other hand, the accuracies for self-administrated samples drop to 95% and 98% respectivelv.
Whether someone catches COVID-22 or not heavily depends on whether he/she has been vaccinated or not. With vaccination, one has a 5% chance of catching COVID-22; while the probability is 22% for the
unvaccinated.
It is estimated about 96% of the general public have been vaccinated and 8 in 10 PC testing samples are collected by testes themselves.
Remember that sensitivity refers to the probability of a positive test, conditioned on truly being infected with the disease while specificity (true negative rate) refers to the probability of a negative test, conditioned
on truly being negative.
Read the description carefully and design a Bayesian network that is suitable to answer queries about one’s COVID-22 status
Specifically, you should:
1. Present your network in a graphical representation and state all the assumptions you have made.
• briefly describe the steps you have followed to reach the final Bayesian Network;
how many parameters are required for your Bayesian network?
list two (conditional or marginal) independent relationships based on your Bayesian network and briefly explain why.
2. Answer the following query by making probabilistic inferences with your Bayesian network. You should provide intermediate steps for the inference results.
q1: Alex has been vaccinated. And Alex has tested positive using an at-home COVID-22 rapid antigen test. How likely Alex is going to get a positive PC test result if he takes a
confirmation test?
q2: Brian has tested positive with an at-home COVID-22 rapid antigen test and negative with a confirming PCR test. How likely is Brian infected with COVID-22?
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