Bayesian Estimation

Abstract

Suppose there are two events that can occur sometime in the future, which we will denote by the letters A and B. For instance, A might be the event that a patient will have his or her blood pressure lowered to “normal” by the treatment about to be given, and B is the event that the patient will remain free from stroke after five years of treatment. We can think of the events by themselves and talk about the probability of each, symbolized

$$Prob\,\left\{ A \right\}\,\,and\,\,Prob\,\left\{ B \right\},$$

or we can consider the probabilities associated with their relationship. Suppose we can lower the patient’s blood pressure with treatment. Then we might expect that the probability of event B is different than if we had failed to lower the blood pressure. We might expect that the probability of event B, given that A has occurred, symbolized

$$Prob\,\left\{ {B|A} \right\},$$

will be greater than unconditional Prob{B}.