Bayesian benefits for binomial applications in practice

Introduction: When it comes to the practice, and teaching, of statistics, the world has primarily focused on what is known as classical or frequentist methods, rather than Bayesian methods.

Scope of the Study: This paper demonstrates some beneficial properties of Bayesian methods within the commonly practiced domain of inference by utilizing consultancy case studies, one concerning an unusual sample size question and one on the detection of mail items with high biosecurity risk material.

Methods: We introduce through practical applications two more aspects of the Bayesian approach which we believe are invaluable to practitioners and instructors. Having in mind readers who may be less familiar with statistical software, we have added Excel instructions which are easy to translate for those who are familiar with any such software.

Findings: These cases reflect two valuable aspects for both practitioners and instructors which are unique to the Bayesian paradigm. They are: 1. including prior information to improve inference and how to apply sensitivity analysis to this inclusion and 2. the effortless inference for functions of parameters, compared with frequentist approaches. These examples involving the binomial parameter have not been considered from this perspective before, are of significant practical value and thus benefit students and instructors of courses teaching Bayesian techniques and endeavoring to include authentic learning experiences.