Bayesian Inference and Diagnosis $($For Type $1$ only$)$

$2\mathrm{.}1.$ Perform Bayesian inference on your network.

Given that a patient exhibits certain symptoms $($e$.$g$.,$ blurred vision, extreme hunger$),$ calculate the updated probability of the patient having the disease $($e$.$g$.,$ Type $1$ diabetes$)$ using Bayes' theorem. $[30$ marks$]$

You will consider if the patient is diagnosed with Type $1$ Diabetes if Yes then a test will be recommended.

$\backslash$table$[[\backslash$table$[[$Increased thirst$],[$and frequent$],[$urination:$]],\backslash$table$[[$Extreme$],[$hunger:$]],\backslash$table$[[$Unintended$],[$weight loss:$]],$Fatigue:,$\backslash$table$[[$Blurred$],[$vision:$]],$Irritability:,$\backslash$table$[[$Slow$-$healing$],[$sores or frequent$],[$infections:$]],\backslash$table$[[$Type $1],[$Diabetes$]]],[$Y$,$N$,$Y$,$Y$,$N$,$N$,$High,?$],[$N$,$Y$,$N$,$Y$,$Y$,$Y$,$Low,?$],[$Y$,$Y$,$Y$,$N$,$N$,$Y$,$Moderate,?$],[$N$,$Y$,$N$,$N$,$Y$,$N$,$Low,?$]]$

Show the steps involved in calculating these probabilities. $[25$ marks$]$

$2\mathrm{.}2.$ Interpret the results of your Bayesian inference: $($For Type $1$ only$)$

How does the presence of one or more symptoms $($evidence$)$ affect the likelihood of the disease? $[10$ marks$]$

Discuss how a CDSS can use these probabilistic results to assist healthcare professionals in making diagnoses $[$Explain in $5$ LINES$].[15$ marks$]$