Nonstationary Gaussian process emulators with covariance mixtures

Duration: 58 mins 35 secs

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Description:	Williamson, D Friday 9th February 2018 - 10:00 to 11:00


Created:	2018-02-12 11:18
Collection:	Uncertainty quantification for complex systems: theory and methodologies
Publisher:	Isaac Newton Institute
Copyright:	Williamson, D
Language:	eng (English)


Abstract:	Routine diagnostic checking of stationary Gaussian processes fitted to the output of complex computer codes often reveals nonstationary behaviour. There have been a number of approaches, both traditional and more recent, to modelling or accounting for this nonstationarity via the fitted process. These have included the fitting of complex mean functions to attempt to leave a stationary residual process (an idea that is often very difficult to get right in practice), using regression trees or other techniques to partition the input space into regions where different stationary processes are fitted (leading to arbitrary discontinuities in the modelling of the overall process), and other approaches which can be considered to live in one of these camps. In this work we allow the fitted process to be continuous by modelling the covariance kernel as a finite mixture of stationary covariance kernels and allowing the mixture weights to vary appropriately across parameter space. We introduce our method and compare its performance with the leading approaches in the literature for a variety of standard test functions and the cloud parameterisation of the French climate model. This is work led by my final-year PhD student, Victoria Volodina.

Abstract:

Routine diagnostic checking of stationary Gaussian processes fitted to the output of complex computer codes often reveals nonstationary behaviour. There have been a number of approaches, both traditional and more recent, to modelling or accounting for this nonstationarity via the fitted process. These have included the fitting of complex mean functions to attempt to leave a stationary residual process (an idea that is often very difficult to get right in practice), using regression trees or other techniques to partition the input space into regions where different stationary processes are fitted (leading to arbitrary discontinuities in the modelling of the overall process), and other approaches which can be considered to live in one of these camps. In this work we allow the fitted process to be continuous by modelling the covariance kernel as a finite mixture of stationary covariance kernels and allowing the mixture weights to vary appropriately across parameter space. We introduce our method and compare its performance with the leading approaches in the literature for a variety of standard test functions and the cloud parameterisation of the French climate model. This is work led by my final-year PhD student, Victoria Volodina.

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