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.