Question

What are prior and posterior probabilities and how are they related? Give some examples where posterior probabilities would be useful.

Answer 1

Prior probability is the probability that an event will fall under a group before you collect the data.

For ex. if 5% of a population has knee pain then the probability that a person drawn at random would have knee pain is 0.05.

Posterior probability is the probability of assigning events to different groups with collected data.

For ex. If 5% of a population has knee pain then the probability that a person drawn at random would have knee pain is 0.05. however, after collecting the data we observe that the proportion in reality for out data is 0.04

Thus, 0.04 is posterior probability

Thus,

Posterior probability = Prior probability + new likelihood