Question

In: Statistics and Probability

Given our discussion in class explain how Bayes Theorem works. In your explanation tell me how...

Given our discussion in class explain how Bayes Theorem works. In your explanation tell me how you go from prior probability estimates to posterior probabilities. What impact does this have on your interpretation of your data?

Solutions

Expert Solution

Bayes' theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event.It  relies on incorporating prior probability distributions in order to generate posterior probabilities.

The below equation is Bayes rule:

also, P(A|B)P(B) = P(B|A)P(A),

Where, P(A|B) is called the posterior; P(B|A) is called the likelihood;P(A) is called the prior;P(B) is called the marginal likelihood;.

The posterior probability is calculated by updating the prior probability using Bayes' theorem.

The posterior probability can be written in the memorable form as

Posterior probability ∝ Likelihood X prior probability.

The posterior probability can also be defined as

Where, the prior probability distribution function is P() and the likelihood is P(X|).

Prior probability represents what is originally believed before new evidence is introduced, and posterior probability takes this new information into account.


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