what does a posterior probability tell you 
bayes theorem can be used in many applications such as medicine finance and economics in finance bayes theorem can be used to update a previous belief once new information is obtained prior probability represents what is originally believed before new evidence is introduced and posterior probability takes this new information into account posterior probability distributions should be a better reflection of the underlying truth of a data generating process than the prior probability since the posterior included more information a posterior probability can subsequently become a prior for a new updated posterior probability as new information arises and is incorporated into the analysis 