Journal Article

Functional Uniform Priors for Nonlinear Modeling

Bornkamp, Björn

2012

Overview

This article considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a prior distribution that is uniform in the space of functional shapes of the underlying nonlinear function and then back‐transform to obtain a prior distribution for the original model parameters. The primary application considered in this article is nonlinear regression, but the idea might be of interest beyond this case. For nonlinear regression the so constructed priors have the advantage that they are parametrization invariant and do not violate the likelihood principle, as opposed to uniform distributions on the parameters or the Jeffrey’s prior, respectively. The utility of the proposed priors is demonstrated in the context of design and analysis of nonlinear regression modeling in clinical dose‐finding trials, through a real data example and simulation.

• Publisher: Blackwell Publishing Inc,Wiley-Blackwell,Blackwell Publishing Ltd
• Subject: Approximation / Bayes Theorem / Bayesian Optimal Design / BIOMETRIC METHODOLOGY / Biometry / Clinical Trials as Topic - statistics & numerical data / Design optimization / Dosage / Dose response relationship / Dose-Finding / Dose-Response / Dose-Response Relationship, Drug / Drug design / Geometric shapes / Humans / Irritable Bowel Syndrome - drug therapy / Likelihood Functions / Linear regression / Mathematical functions / Mathematical independent variables / Mathematical models / Models, Statistical / Musical intervals / Nonlinear Dynamics / Nonlinear equations / nonlinear models / Nonlinear Regression / Packing Numbers / Probabilities / statistical models