Introduction to Bayesian methods II: fundamental concepts

The use of Bayesian design and analysis is burgeoning. In this introduction to Bayesian methods, we provide basic examples of Bayesian thinking and formalism on which more complicated and comprehensive approaches are built. These include adjusting estimates using related information, the use of Bayes theorem in diagnostic testing, the relationship of the prior and posterior distributions for situations where both the data and prior distribution are Gaussian, and the key steps in a Bayesian analysis. If Bayesian methods are carefully developed and applied, they have excellent objective (i.e., frequentist) properties, providing marvelous tools to help improve the FDA regulatory process.