ABSTRACT
While both frequentist and Bayesian statisticians use prior information, the former use a prior in the design of experiments only, whereas the latter uses priors for both experimental designs and statistical inferences on the parameter or the drug effect. Another main difference between the Bayesian and frequentist approaches is that Bayesianism emphasizes the importance of information synergy from different sources. There are different statistical paradigms or theoretical frameworks, which reflect different philosophies or beliefs. These differences have provoked quite a few controversies. However, within each paradigm or axiom system, consistency and completeness are expected. This chapter focuses on the Bayesian paradigm. For modeling it is often convenient and appropriate to use Bayesian statistical models hierarchically with several levels of conditional prior distributions. Bayes’ factor, posterior distribution, and credible intervals are commonly used in Bayesian inference. Bayesian inference can be used in model selections. Bayesian decision-making is a probabilistic optimization in which minimization of the defined loss function is the goal.
