## Bayesian Design for the Normal Linear Model with Unknown Error Variance

September, 1996

Tech Report

### Author(s)

Isabella Verdinelli

### Abstract

Most of the Bayesian theory of optimal experimental design, for the normal linear model, has been developed under the restrictive assumption that the variance is known. In special cases, insensitivity of specific design criteria to specific prior assumptions on the variance has been demonstrated, but a general result to show the way in which Bayesian optimal designs are affected by prior information about the variance is lacking.

This paper stresses the important distinction between expected utility functions and optimality criteria, examines a number of expected utility functions - some of which possess interesting properties, and deserve wider use - and derives the relevant Bayesian optimality criteria under normal assumptions. This unifying setup is useful for proving the main result of the paper, that clarifies the issue of designing for the normal linear model with unknown variance.