Uncertainty in financial models of large and complex government projects
Government financial models, a particular type of deterministic computer model, are created in order to estimate the cost of expensive projects with large time frames. The model is a function of many inputs, most of which are taken to be known. However the value of a small number of inputs X is unknown. Whilst the precise value of X is unknown, subjective knowledge about X can be represented by a joint probability distribution G(x). As a result of the uncertainty in X, the scalar output of the financial model is the random variable, Y. The main focus of this thesis is in learning about the uncertainty in Y that results from uncertainty in X (uncertainty analysis), and in determining which elements of X are most (and least) important in driving the uncertainty in Y (sensitivity analysis). In principle both uncertainty and sensitivity analyses can be conducted using Monte Carlo. This method requires a large number of model evaluations. We are interested in the case where the computer model is too computationally expensive to make Monte Carlo practical. We consider a Bayesian approach, which uses the Gaussian Process prior for unknown functions in order to make inference about the computer model itself, using a small number of model evaluations. We then use this information about the structure of the computer model in order to perform uncertainty and sensitivity analyses using relatively few runs of the model. In this thesis, we adapt the standard Gaussian Process prior in order to utilize the additional information we have about the structure of government financial models. 'We develop methodology for calculating measures of uncertainty and sensitivity based upon a Gaussian Process model. The methodology also utilizes the additional structural information within government financial models. Finally, we develop elicitation methodology for use in determining the joint probability distribution G(x). We provide an example from the Private Finance Initiative.