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Solutions: Bayes’ Theorem – in a nutshell

March 21, 2019

Solution to Exercise

Question a. The formula for Bayes’ Theorem can be represented as:

Updated (posterior) probability given new evidence = ab/ [ab+ c (1-a)]

a is the probability that the hypothesis is true before encountering new evidence. This is called the prior probability.

b is the probability of encountering the evidence given that the hypothesis is true.

c is the probability of encountering the evidence given that the hypothesis is not true.

Question b. P (HIE) = P (H). P (EIH) / [P (H). P (EIH) + P (EIH’) . P (1 – P (H’)]

Question c. P (H) is the probability that the hypothesis is true before encountering the new evidence. This is the prior probability (also represented as a). P (EIH) is the probability of encountering the evidence given that the hypothesis is true (also represented as b). P (EIH’) is the probability of encountering the evidence given that the hypothesis is not true (also represented as c).

Question d. No, P (HIE) is not equal to P (EIH).

P (HIE) = P (H). P (EIH) / [P (H). P (EIH) + P (EIH’) . P (1 – P (H)]

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