ECS647U / ECS773P
Bayesian Decision and Risk (BDRA)
Semester B, 2022
Coursework 2 –Bayes Theorem and Bayesian Learning
Deadline: Thursday 14th April 2022
This coursework is based on a fictitious virus called SARS-Cov-4 which causes a
disease called Covid-24.
Question 1
Despite assumptions to the contrary, it is possible to test positive using a PCR
test, and be diagnosed as having Covid-24, even if someone has not been
infected with SARS-Cov-4 and has no symptoms of the disease. The
government’s policy recommendation is that people testing positive should self
isolate for 10 days. A number of factors might influence the reliability of the
PCR test such as cross reactivity with other viruses, lab mix-ups and faulty/non-
sterile testing equipment.
a) Calculate the posterior probability of a random person, with no Covid-24 symptoms,
actually having SARS-Cov-4, P(SARS-Cov-4 = True | PCR Test = Positive), given the
following information [10]:
P(SARS-Cov-4 = True) = 0.02
P(PCR Test = Positive | SARS-Cov-4 = True) = 0.9
P(PCR Test = Positive | SARS-Cov-4 = False) = 0.2
b) Calculate the marginal probability of a false positive result [5]:
P(False positive = Yes | PCR Test, SARS-Cov-4)
c) Use the Binomial distribution to calculate the number of false positives, f, in the
population, where p = P(False positive = Yes | PCR Test, SARS-Cov-4). [5]
~(, = 50 )
d) What would the implications of random SARS-Cov-4 screening be on the self-
isolation rate in an adult population of 50 million people subject to such screening? [5]
Question 2
This question is based on a fictitious therapeutic treatment and a fictitious vaccine for
Covid-24.
Five groups of independent researchers in different countries have treated
patients using a proposed therapeutic cure for severe cases of Covid-24. The
data from these experiments is given below, where the number of patients in
experiment i is in , the number of patients that died is ix and is the
probability of a patient dying in a given experiment.
Experiment =
1 100 20 0.20
2 115 25 0.22
3 37 6 0.16
4 22 6 0.27
5 30 9 0.30
pooled 304 66 0.22
a) You are performing a meta-analysis to combine all of the data from these studies to
assess the effectiveness of the therapeutic. To do so you must build a BN parameter
learning model with the following configuration:
~(, , 0,1)
~(0,200)
~(0,200)
~(, )
Calculate ( |, , , , ) where is the estimated probability of death for the
therapeutic treatment. [15]
b) Current policy for treatment of Covid-24 is to rely on prior vaccination. Assuming
if someone is already vaccinated there is a 20% probability of death if suffering
from severe Covid-24. Calculate the probability than the therapeutic cure is
better/worse than vaccination at reducing the probability of death from severe
Covid-24. [5]
c) Would you recommend switching to use of the therapeutic or recommend
continuing with vaccination policy? [5]
Notes:
Where relevant use AgenaRisk to specify BNs and perform the necessary
calculations. In your answer show the relevant probability distributions as
screen shots and show the necessary summary statistics and probabilities needed
for your answer.
In Q1 assume ‘no symptoms’ is simply background information and plays no
formal role in the probability evaluation.
For all models use simulation settings: Max number of iterations = 50 and
simulation convergence 0.001. Also use integer type nodes for Binomial
distributions.
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