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SUMMARY:Emulating complex codes: The implications of using separable covar
 iance functions - Rougier\, J (University of Bristol)
DTSTART:20110905T153000Z
DTEND:20110905T160000Z
UID:TALK32655@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Emulators are crucial in experiments where the computer code i
 s sufficiently expensive that the ensemble of runs cannot span the paramet
 er space. In this case they allow the ensemble to be augmented with additi
 onal judgements concerning smoothness and monotonicity. The emulator can t
 hen replace the code in inferential calculations\, but in my experience a 
 more important role for emulators is in trapping code errors. \nThe theory
  of emulation is based around the construction of a stochastic processes p
 rior\, which is then updated by conditioning on the runs in the ensemble. 
 Almost invariably\, this prior contains a component with a separable covar
 iance 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. \nThis is an alarmi
 ngly strong prior judgement about the computer code\, ruling out interacti
 ons. But\, like the property of stationarity\, it does not survive the con
 ditioning process. The cautionary response is to include several regressio
 n terms in the emulator prior.\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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