Tony O'Hagan - Academic pages - Abstracts

## Bayesian Inference for the
Uncertainty Distribution of Computer Model Outputs

Jeremy Oakley and Anthony O'Hagan

*University of Sheffield*

**Publication details: **
*Biometrika* **89**, 769-784, 2002.

### Abstract

We consider a problem of inference for the output of a computationally
expensive computer model. We suppose that the model is to be used in a
context where the values of one or more inputs are uncertain, so that the
input configuration is a random variable. We require to make inference
about the induced distribution of the output. This distribution is called
the uncertainty distribution, and the general problem is known to users of
computer models as uncertainty analysis. Specifically, we develop Bayesian
inference for the distribution and density functions of the model output.
Modelling the output, as a function of its inputs, as a Gaussian process,
we derive expressions for the posterior mean and variance of the
distribution and density functions, based on data comprising observed
outputs at a sample of input configurations. We show that direct
computation of these expressions may encounter numerical difficulties. We
develop an alternative approach based on simulating approximate
realisations from the posterior distribution of the output function. Our
methods are illustrated using a model describing the effective dose
received by individuals on ingesting radioactive iodine.

**Keywords: **Computer experiment; Gaussian process; Uncertainty analysis.

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Updated: 22 November 2002
Maintained by: Tony O'Hagan