Bayesian uncertainty analysis for complex physical systems modelled by computer simulators with applications to tipping points

In this paper we present and illustrate basic Bayesian techniques for the uncertainty analysis of complex physical systems modelled by computer simulators. We focus on emulation and history matching and also discuss the treatment of observational errors and structural discrepancies in time series. We exemplify such methods using a four-box model for the termohaline circulation. We show how these methods may be applied to systems containing tipping points and how to treat possible discontinuities using multiple emulators.

[1]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[2]  David Wooff,et al.  Bayes Linear Statistics: Theory and Methods , 2007 .

[3]  Jonathan Rougier,et al.  Probabilistic Inference for Future Climate Using an Ensemble of Climate Model Evaluations , 2007 .

[4]  Michael Goldstein,et al.  Small Sample Bayesian Designs for Complex High-Dimensional Models Based on Information Gained Using Fast Approximations , 2009, Technometrics.

[5]  Michael Goldstein,et al.  Reified Bayesian modelling and inference for physical systems , 2009 .

[6]  Robin K. S. Hankin,et al.  Towards the probability of rapid climate change , 2006 .

[7]  M. Goldstein.  Bayes Linear Analysis , 2006 .

[8]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[9]  J. Rougier,et al.  Bayes Linear Calibrated Prediction for Complex Systems , 2006 .

[10]  Anthony O'Hagan,et al.  Diagnostics for Gaussian Process Emulators , 2009, Technometrics.

[11]  F. Pukelsheim.  The Three Sigma Rule , 1994 .

[12]  Michael Goldstein,et al.  Subjective Bayesian Analysis: Principles and Practice , 2006 .

[13]  A. OHagan,et al.  Bayesian analysis of computer code outputs: A tutorial , 2006, Reliab. Eng. Syst. Saf..

[14]  Michael Goldstein,et al.  History matching for exploring and reducing climate model parameter space using observations and a large perturbed physics ensemble , 2013, Climate Dynamics.

[15]  Henry Stommel.  Thermohaline Convection with Two Stable Regimes of Flow , 1961 .

[16]  Ian Vernon,et al.  Galaxy formation : a Bayesian uncertainty analysis. , 2010 .

[17]  Thomas Slawig,et al.  A low-order model for the response of the Atlantic thermohaline circulation to climate change , 2004 .

[18]  A. O'Hagan,et al.  Bayesian emulation of complex multi-output and dynamic computer models , 2010 .

[19]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[20]  A. O'Hagan,et al.  Gaussian process emulation of dynamic computer codes , 2009 .

[21]  Robin Tokmakian,et al.  On the Use of Emulators with Extreme and Highly Nonlinear Geophysical Simulators , 2012 .