Linear and generalized linear mixed effects models

Abstract

We often use probabilities informally to express our information and beliefs about unknown quantities. However, the use ofprobabilities to express information can be made formal: In a precise mathematical sense, it can be shown that probabilitiescan numerically represent a set of rational beliefs, that there is a relationship between probability and information, andthat Bayes’ rule provides a rational method for updating beliefs in light of new information. The process of inductive learningvia Bayes’ rule is referred to as Bayesian inference.