PARAMETER FITTING FOR UNCERTAIN MODELS - MODELING UNCERTAINTY IN SMALL MODELS

In uncertainty analysis distributions are placed over parameters in th e model which is to be analysed. These distributions are sometimes sai d to express uncertainty in the parameter values, conditional on the m odel being correct. This paper takes the view that distributions over model parameters should express the unconditional uncertainty in the f unctional relationships posited by the model. For small models, effect ive procedures are given to generate distributions over model paramete rs which account for this type of uncertainty. A model is regarded as a function from one observation space to another. Uncertainty distribu tions over the image space, conditional on various values from the dom ain space are assumed to be given, e.g. via expert judgement. The prob lem is to define a unique distribution over the parameter space of the model which best utilises these conditional distributions. Two soluti on concepts are distinguished. A 'classical' solution uses an analogue of the log likelihood ratio to define a unique distribution on the mo del's parameter space. The solution best fits the expert conditional d istributions when the latter are projected onto the parameter space of the model. A Bayesian solution considers the conditional distribution s as data in an updating scheme. These two solution concepts are inter preted as correctly capturing different legitimate senses of the word 'solution'. Data from recent applications in atmospheric dispersion mo delling and dose-response modelling are discussed.