On Bayesian Data Analysis

TL;DR

This paper introduces Bayesian statistics, explaining core concepts, prior selection, asymptotic properties of Bayes estimators, and testing methods, advocating for Bayesian modeling in statistical analysis.

Contribution

It provides a comprehensive overview of Bayesian methods, including prior determination, asymptotic justification, and testing, serving as an accessible introduction to Bayesian data analysis.

Findings

Bayesian estimators have strong asymptotic properties.

Prior selection significantly influences Bayesian inference.

Bayesian testing offers a coherent framework for hypothesis testing.

Abstract

This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic arguments in favour of using Bayes estimators. The testing aspects of Bayesian inference are also examined in details.