Bayesian Analysis of the Linear Model Subject to Linear Inequality Constraints

Abstract

This article considers the general linear model when the parameter space is subject to linear inequality constraints. A Bayesian analysis of this model is presented using a natural conjugate prior of the mixed type. Expressions are given for the probability that constraints are binding and for the distribution of the parameters. When prior information about the parameters is vague, the Bayesian and sampling methods of model selection are compared. The techniques are applied to a time series of temperatures of a chemical reaction.

Key Words:

• Bayesian analysis
• Binding constraint
• Linear model
• Mixed prior distribution
• Restricted parameter space