Functional Uniform Priors for Nonlinear Modeling
Article first published online: 27 JUL 2012
© 2012, The International Biometric Society
Volume 68, Issue 3, pages 893–901, September 2012
How to Cite
Bornkamp, B. (2012), Functional Uniform Priors for Nonlinear Modeling. Biometrics, 68: 893–901. doi: 10.1111/j.1541-0420.2012.01747.x
- Issue published online: 26 SEP 2012
- Article first published online: 27 JUL 2012
- Received August 2011. Revised December 2011. Accepted January 2012.
- Bayesian Optimal Design;
- Nonlinear Regression;
- Packing Numbers
Summary 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.