Posteriorization

Posteriorization is a term used in Bayesian statistics to describe the process of updating prior beliefs about parameters in light of new evidence or data. This update results in a posterior distribution, which represents the revised beliefs after considering the observed data. The core of posteriorization lies in Bayes' theorem, a fundamental equation that formalizes this update. Bayes' theorem states that the posterior probability of a hypothesis is proportional to the likelihood of observing the data given the hypothesis, multiplied by the prior probability of the hypothesis.

In practice, posteriorization involves combining a prior distribution, which quantifies initial uncertainty about parameters before any data is observed, with the likelihood function, which describes how probable the observed data is for different values of the parameters. The outcome is the posterior distribution, which is a probability distribution that reflects the updated understanding of the parameters. This posterior distribution can then be used for various statistical inferences, such as estimating parameter values, calculating credible intervals, or making predictions about future observations. The process is iterative; if new data becomes available, the current posterior distribution can serve as the prior for the next round of posteriorization.