Functional uniform prior distributions for nonlinear regression
Seminar Room 1, Newton Institute
In this talk I will consider the topic of finding prior distributions in nonlinear modelling situations, that is, when a major component of the statistical model depends on a non-linear function. Making use of a functional change of variables theorem, one can derive a 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 non-linear regression in the context of clinical dose-finding trials. Here the so constructed priors have the advantage that they are parametrization invariant as opposed to uniform priors on parameter scale and can be calculated prior to data collection as opposed to the Jeffrey’s prior. I will investigate the priors for a real data example and for calculation of Bayesian optimal designs, which require the prior distribution to be available before data collection has started (so that classical objective priors such as Jeffreys priors cannot be used).