Bayesianism: From the casuistic to the historical

Abstract

This document fundamentally presents two aspects related to the Bayesian matter: i) two cases of application of Bayesian epistemology, and, ii) a summarized and intuitive exposition of the formality of Bayesian techniques and its core, Bayes' theorem, culminating with a brief historical review and a conception of Bayesian epistemology., Based on documentary analysis and bibliographic review method, a general characterization of a Bayesian analysis context describes two comprehensive cognitive situations of that context, the Bayesian inference and the Bayesian decision theory; In addition, general Bayesian applications are discussed and then two specific cases of application are given: in daily medical practice, and in the "plan-evaluation" of social projects. A short section in a very basic way exposes Bayesian methodological formalities by interpreting Bayes' theorem and the concept of likelihood. Finally, a closing section includes a historical overview and an integrative definition of the main components of Bayesian epistemology. The consolidation of Bayesian epistemology has required the contribution of many authorities in the matter; two of the most influential pioneers mentioned in this document are Aykac and Brumat (1977) and Lindley (1977). In conclusion, Bayesian epistemology is presented as a theory of learning in uncertainty regarding random and uncertain events or states of things, of nature or reality, learning or new knowledge that is expressed in terms of probabilities.