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Emulating complex codes: The implications of using separable covariance functions

Monday 5th September 2011 - 16:30 to 17:00
INI Seminar Room 1
Session Title: 
Computer Simulators and Physical Experiments II
Session Chair: 
A. O'Hagan
Emulators are crucial in experiments where the computer code is sufficiently expensive that the ensemble of runs cannot span the parameter space. In this case they allow the ensemble to be augmented with additional judgements concerning smoothness and monotonicity. The emulator can then replace the code in inferential calculations, but in my experience a more important role for emulators is in trapping code errors.

The theory of emulation is based around the construction of a stochastic processes prior, which is then updated by conditioning on the runs in the ensemble. Almost invariably, this prior contains a component with a separable covariance function. This talk considers exactly what this separability implies for the nature of the underlying function. The strong conclusion is that processes with separable covariance functions are second-order equivalent to the product of second-order uncorrelated processes.

This is an alarmingly strong prior judgement about the computer code, ruling out interactions. But, like the property of stationarity, it does not survive the conditioning process. The cautionary response is to include several regression terms in the emulator prior.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons