This thesis investigates methods of modelling problems containing uncertainty, paying particular attention to situations where there is hole empirical data and the modeller chooses to employ subjective expert assessments. In chapter 1 we examine the historical and philosophical underpinnings of subjective probability, discuss how it can be used in practical situations and investigate some of the typical errors associated with eliciting expert assessments. We describe an experiment in which experts assess multi-outcome events with which they are familiar and examine whether they suffer from the same types of assessment errors as naive subjects tend to exhibit As a foundation for our further experiments we discuss the methods and procedures which other practitioners have adopted for eliciting expert judgements and examine how conflicting assessments might be resolved into a coherent position. Chapter 2 investigates ways in which univariatc uncertainty can be quantified and modelled. We conduct an experiment on the elicitation of means and variances for a variety of real distributions and procedures suggested in previous studies. The standard methods of representing random variables with differential equations, series expansions, transformations and inverse functions are discussed and we develop a new functional form for simulation studies. This NB function is both more flexible and computationally faster than the standard alternatives. We have also developed interactive software for the elicitation and quantification of a variable in this NB functional form and describe an experiment to verify this approach. Chapter 3 develops the univariate approaches of chapter 2 for applications involving dependent variables. We first discuss the standard methods of representing multivariate distributions and highlight their limitations. Having examined the requirements of a multivariate representation suitable for simulation and expert elicitation, we develop two approaches based upon the NB functions already described and dependence measures. These are compared with various standard forms, fitting them to both theoretical and real distributions, with some very promising results. Finally we describe an experiment in which we subjectively elicit measures of dependence for a number of real distributions, comparing the accuracy and acceptability of the various techniques.

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