代写ECS647U课程、代写Python，c++程序

日期：2022-04-15 11:00

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.