The ultimate goal of statistics is to provide an inference about a parameter theta (q) given some observations x related to q through a probability distribution f(x|q ). The basis of statistical inference is fundamentally an inversion process, since it aims at deriving effects from causes by taking into account the probabilistic nature of the model and the influence of totally random (i.e. unexplained) factors. In both its discrete and continuous versions, Bayes' theorem formalizes this inversion, as does the notion of the likelihood function L(x|q), and as such is the unique coherent paradigm which respects the inversion perspective:

P(x)´P(q|x) = P(qx) = P(q)´P(x|q)

Table of contents

General Framework For Bayesian Statistics
The Bayesian Approach
The Prior Distribution
The Likelihood Principle/Function
An Example of Bayesian Estimation at Work
Bayesian Decision Theory
Benefits and Contras of The Bayesian Choice
Online Bayesian Calculators
A Bayesian Reading List

This page was last updated on 05/25/05