Tony O'Hagan - Academic pages - Abstracts

## Probabilistic Sensitivity Analysis of Complex Models:
A Bayesian Approach

Jeremy E. Oakley and Anthony O'Hagan

*Department of Probability and Statistics, University of Sheffield,
Sheffield, England*

**Publication details: **
*Journal of the Royal Statistical Society,
Series B* **66**, 751-769, 2004.

### Abstract

In many areas of science and technology, mathematical models are built
to simulate complex real-world phenomena. Such models are typically
implemented in large computer programs, and are also very complex,
such that the way that the model responds to changes in its inputs
is not transparent. Sensitivity analysis is concerned with understanding
how changes in the model inputs influence the outputs. This may be
motivated simply by a wish to understand the implications of a complex
model, but often arises because there is uncertainty about the true
values of the inputs that should be used for a particular application.

A broad range of measures have been advocated in the literature to
quantify and describe the sensitivity of a model's output to variation
in its inputs. In practice the most useful measures are those based
on formulating uncertainty in the model inputs by a joint probability
distribution and then analysing the induced uncertainty in outputs,
an approach known as probabilistic sensitivity analysis. We present
a Bayesian framework which unifies the various tools of probabilistic
sensitivity analysis.

The Bayesian approach is computationally
highly efficient. It allows effective sensitivity analysis to be
achieved using far smaller numbers of model runs than standard Monte Carlo
methods. Furthermore, all measures of interest may be computed from
a single set of runs.

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Updated: 4 August 2004
Maintained by: Tony O'Hagan