Numerical Analysis and Computation Commons^™

Bayesian Statistics: The Fundamental Theorem, Carolyn Rhodes

Honors Theses

The problem of the foundation of statistics is to state a set of principles which entail the validity of all correct statistical inference, and which do not imply that any fallacious inferences is valid. This sentence describes the purpose of much writing on statistical inferences, in general, and Bayesian statistics, in particular. Bayesian statistics was first introduced in a publication by Thomas Bayes in The London Philosophical Transactions, volumes 53 and 54 for the years 1763 and 1764, after Bayes' death in 1761. However, since the entire statistical research of Bayes' involves enormous study, this paper will limit itself to …