Basic MUCM reading list – AO’H suggestions

O'Hagan, A. (2006). Bayesian
analysis of computer code outputs: a tutorial.
*Reliability Engineering and System Safety ***91**,
1290–1300.

This is a very simplified presentation of the basic ideas of MUCM from the full Bayesian perspective. It is written for modellers and model users rather than statisticians, so aims for intuitive understanding of how Gaussian process emulators work, rather than technical depth. It does give references to the more technical literature. It assumes some understanding of uncertainty analysis and sensitivity analysis.

Kennedy, M. C. and O'Hagan, A.
(2001). Bayesian
calibration of computer models
(with discussions). *Journal of the Royal Statistical Society* *B
***63**, 425–464.

Additional material that was cut from the paper here and here.

This is the classic paper which explicitly introduced the idea of a model inadequacy term to represent the difference between a computer code’s output (using the ‘best’ input settings) and reality. Although the technical details of Bayesian calibration are quite dense, it begins with a good presentation of the background to MUCM – what the problems are that concern modellers and model users, the sources of uncertainty that arise when tackling such problems, and many aspects of modelling with Gaussian processes.

Kennedy, M. C., Anderson, C. W., Conti,
S. and O'Hagan, A. (2006). __Case
studies in
Gaussian process modelling of computer codes__.
*Reliability Engineering and System Safety ***91**,
1301–1309.

Another paper aimed at modellers and model users. It is useful for people interested in MUCM because it shows how the Gaussian process emulators are used in practice and how they can actually give insight into the way the model works.

Sacks, J., Welch, W.J., Mitchell, T.J.
and Wynn, H.P. (1989). __Design and analysis
of computer experiments.__ *Statistical Science* **4**,
409–435, with discussions in __Sta Sci__
and __Technometrics.__

This is useful for historical
understanding. Research in DACE (design and analysis of computer
experiments) was the forerunner of BACCO (Bayesian analysis of
computer code outputs), and hence of MUCM. The emphasis was on
emulating the model (although the term ‘emulator’ was not then
used) in order to predict and optimise the output, and there was much
research into constructing suitable designs. Although the ideas of
uncertainty analysis and sensitivity analysis did attract some
attention, they (together with calibration) are more associated with
the later systematic Bayesian developments of BACCO.

Also here, you can find a recent paper on multioutput emulation, applied to emulating a dynamic model.