An Interactive Application Demonstrating Frequentist and Bayesian Inferential Frameworks

Providing students insights into both the frequentist and Bayesian inferential frameworks is challenging as simple textual instructions or mathematical formulations do not capture the intricacies and subtleties of these concepts, particularly for beginners. The paper presents a simple, user-friendly, and interactive application in the R Shiny environment to communicate the key ideas under both inferential methods. It employs simulation and repeated experiments to demonstrate the frequentist’s concept of relative frequencies through sampling distribution, sample estimator, and confidence intervals. On a single dataset, it calculates the maximum likelihood estimates in the frequentist framework and applies null hypothesis significance testing (NHST). Similarly, the application simulates data to illustrate the likelihood and prior distribution, the resulting posterior distribution, and the highest density intervals (credible intervals) in the Bayesian context. A practical scenario demonstrates the Markov chain Monte Carlo (MCMC) approach to solve a Bayesian problem to derive the posterior distribution and highlights essential convergence diagnostics and output analysis (CODA). The application allows learners to interact and enable a multitude of scenarios with the help of instantaneous simulations, variations of inputs, and a dynamic graphical interface. It supports learners in understanding principles and analytical approaches of both inferential methods and targets students from beginner to advanced levels. Estimating the prevalence of the disease in a population is used to review the underlying theories of the frequentist and Bayesian methods to solve the problem. It considers the distribution of the disease state as a binomial distribution and the subjective knowledge of the parameter as a beta distribution (a conjugate prior). With specific notes and lesson plans, the article describes the fundamentals and illustrates the similarities and differences in methodologies, outcomes, and interpretations between the two inferential frameworks.