What is Bayesian Probability?
Bayesian probability, also known as evidential probability, is the process of adding prior probability to a hypothesis and adjusting that probability as new information becomes available. Unlike traditional frequentist probability which only accounts for the previous frequency of an event to predicate and outcome, the Bayesian model begins with an initial set of subjective assumptions (prior probability) and adjusts them accordingly through trial and experimentation (posterior probability). Instead of only rejecting or failing to reject a null hypothesis, Bayesian probability allows someone to quantify how much confidence they should have in a particular result.
Bayesian Probability in Practice:
Traditional probability theory can only really answer yes and no questions, by rejecting a null hypothesis or accepting an alternative hypothesis. Bayesian probability’s dynamic processing of guessing and then testing those guesses with statistical tools offers more flexibility. With Bayesian models, a proposition is neither simply true or false, but rather X% true or false, or X% better or worse than Y.
For example, a pharmaceutical company is testing a new drug. They need to know how much better or worse the new product works in comparison to existing treatments, rather than simply a traditional null hypothesis of “does this drug cure an ailment or not?”