Predictive Inference Tools for Researchers

Abstract

An obstacle to widespread employment of Bayesian predictive inference in scientific re-search is the lack of suitable computing tools. In this thesis I document several established useful models, and provide an applicable set of tools for statisticians. For each of the in- cluded models, some basic notes on mathematical derivation are presented, and predictive inference is illustrated with examples. For the details of the models and some of the exam- ples I relied primarily on Seymour Geisser’s Predictive Inference: An Introduction (1993) [3] and Peter D. Hoff’s A First Course in Bayesian Statistical Methods (2009) [5]. An R package has been developed, the main purpose of which is to provide the researcherwith a means of generating samples from predictive distributions. So for all the models, the package includes predictive sample generators. For those models with analytical solutions, density and distribution functions are also provided. The standard R naming convention for these function classes has been adopted: density functions are prefixed with the letter“d,”distribution functions with the letter“p,”and sample generation functions with the letter “r.” Also included in all function names is the abbreviation “pred” (for predictive) and an initialism or abbreviation identifying the model itself. For example, the density function for the Beta-Binomial model is named“dpredBB().”The R code for each function is included in the Appendix.