This paper is from Session 4I: Integrating Bayesian methods with traditional statistics education

which comes under Topic 4: Statistics education at the post secondary (tertiary) level

Other papers under session 4I ... 4I1: Psychology students’ understanding of elementary Bayesian inference 4I3: The very beginning of a class on inference: classical vs Bayesian 4I4: Teaching young grownups how to use Bayesian networks

(Tuesday 13th, 14:00-16:00)

Comparing the Bayesian and likelihood approaches to inference: a graphical approach

Presenter

• Bill Bolstad (University of Waikato, New Zealand)

Abstract

Both likelihood inference and Bayesian inference arise from a surface defined on the inference universe which is the Cartesian product of the parameter space and the sample space. Likelihood inference uses the sampling surface which is a probability distribution in the sampling dimension only. Bayesian inference uses the joint probability distribution defined on the inference universe The likelihood function and the Bayesian posterior distribution come from cutting the respective surfaces with a (hyper)plane parallel to the parameter space and through the observed sample values. Unlike the likelihood function, the posterior distribution always will be a probability distribution. This is responsible for the different choices of estimators, and the different way the two approaches have of dealing with nuisance parameters. In this paper we present a graphical approach for teaching the difference between the two approaches.

Other papers under session 4I ... 4I1: Psychology students’ understanding of elementary Bayesian inference 4I3: The very beginning of a class on inference: classical vs Bayesian 4I4: Teaching young grownups how to use Bayesian networks