A patient goes to the doctor for a medical condition, the doctor suspects three diseases as...

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A patient goes to the doctor for a medical condition, the doctor suspects three diseases as the cause of the condition. The three diseases are D1, D2, D3, which are independent of each other. There are four symptoms S1, S2, S3, S4 which the doctor wants to check for their presence in order to find the most probable cause of the condition. The symptoms are conditionally dependent to the three diseases as follows: S1 depends on D1, and D2, S2 depends only on D1. S3 depends on D1 and D3, whereas S4 depends only on D3. Assume all random variables are Boolean, they are either 'true' or 'false'. a) Which of the following Bayesian networks (1 or 2) represents the above problem. 1. S1 D1 S2 D2 S3 D3 S4 2. S1 D1 b) Write down the expression for the joint probability distribution, P (D1, D2, D3, S1, S2, S3, S4), as a product of conditional probabilities. c) What is the number of independent parameters that is required to describe this joint distribution? d) Assume there were no conditional independence between the variables, how many independent parameters would be required then? S2 D2 S3 D3 S4 A patient goes to the doctor for a medical condition, the doctor suspects three diseases as the cause of the condition. The three diseases are D1, D2, D3, which are independent of each other. There are four symptoms S1, S2, S3, S4 which the doctor wants to check for their presence in order to find the most probable cause of the condition. The symptoms are conditionally dependent to the three diseases as follows: S1 depends on D1, and D2, S2 depends only on D1. S3 depends on D1 and D3, whereas S4 depends only on D3. Assume all random variables are Boolean, they are either 'true' or 'false'. a) Which of the following Bayesian networks (1 or 2) represents the above problem. 1. S1 D1 S2 D2 S3 D3 S4 2. S1 D1 b) Write down the expression for the joint probability distribution, P (D1, D2, D3, S1, S2, S3, S4), as a product of conditional probabilities. c) What is the number of independent parameters that is required to describe this joint distribution? d) Assume there were no conditional independence between the variables, how many independent parameters would be required then? S2 D2 S3 D3 S4

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To determine the most probable cause of the patients condition among the three diseases D1 D2 D3 the ... View the full answer