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55
Probabilistic inference for future climate using an ensemble of climate model evaluations
 Climatic Change
, 2007
"... This paper describes an approach to computing probabilistic assessments of future climate, using a climate model. It clarifies the nature of probability in this context, and illustrates the kinds of judgements that must be made in order for such a prediction to be consistent with the probability cal ..."
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Cited by 23 (8 self)
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This paper describes an approach to computing probabilistic assessments of future climate, using a climate model. It clarifies the nature of probability in this context, and illustrates the kinds of judgements that must be made in order for such a prediction to be consistent with the probability calculus. The climate model is seen as a tool for making probabilistic statements about climate itself, necessarily involving an assessment of the model’s imperfections. A climate event, such as a 2◦C increase in global mean temperature, is identified with a region of ‘climatespace’, and the ensemble of model evaluations is used within a numerical integration designed to estimate the probability assigned to that region.
Lightweight emulators for multivariate deterministic functions
 FORTHCOMING IN THE JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
, 2007
"... An emulator is a statistical model of a deterministic function, to be used where the function itself is too expensive to evaluate withintheloop of an inferential calculation. Typically, emulators are deployed when dealing with complex functions that have large and heterogeneous input and output sp ..."
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Cited by 19 (5 self)
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An emulator is a statistical model of a deterministic function, to be used where the function itself is too expensive to evaluate withintheloop of an inferential calculation. Typically, emulators are deployed when dealing with complex functions that have large and heterogeneous input and output spaces: environmental models, for example. In this challenging situation we should be sceptical about our statistical models, no matter how sophisticated, and adopt approaches that prioritise interpretative and diagnostic information, and the flexibility to respond. This paper presents one such approach, candidly rejecting the standard Smooth Gaussian Process approach in favour of a fullyBayesian treatment of multivariate regression which, by permitting sequential updating, allows for very detailed predictive diagnostics. It is argued directly and by illustration that the incoherence of such a treatment (which does not impose continuity on the model outputs) is more than compensated for by the wealth of available information, and the possibilities for generalisation.
The KnowledgeGradient Policy for Correlated Normal Beliefs
"... We consider a Bayesian ranking and selection problem with independent normal rewards and a correlated multivariate normal belief on the mean values of these rewards. Because this formulation of the ranking and selection problem models dependence between alternatives’ mean values, algorithms may util ..."
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Cited by 19 (14 self)
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We consider a Bayesian ranking and selection problem with independent normal rewards and a correlated multivariate normal belief on the mean values of these rewards. Because this formulation of the ranking and selection problem models dependence between alternatives’ mean values, algorithms may utilize this dependence to perform efficiently even when the number of alternatives is very large. We propose a fully sequential sampling policy called the knowledgegradient policy, which is provably optimal in some special cases and has bounded suboptimality in all others. We then demonstrate how this policy may be applied to efficiently maximize a continuous function on a continuous domain while constrained to a fixed number of noisy measurements.
Practical bayesian optimization of machine learning algorithms
, 2012
"... In this section we specify additional details of our Bayesian optimization algorithm which, for brevity, were omitted from the paper. For more detail, the code used in this work is made publicly available at ..."
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Cited by 14 (1 self)
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In this section we specify additional details of our Bayesian optimization algorithm which, for brevity, were omitted from the paper. For more detail, the code used in this work is made publicly available at
Bayesian Guided Pattern Search for Robust Local Optimization
, 2008
"... Optimization for complex systems in engineering often involves the use of expensive computer simulation. By combining statistical emulation using treed Gaussian processes with pattern search optimization, we are able to perform robust local optimization more efficiently and effectively than using ei ..."
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Cited by 13 (6 self)
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Optimization for complex systems in engineering often involves the use of expensive computer simulation. By combining statistical emulation using treed Gaussian processes with pattern search optimization, we are able to perform robust local optimization more efficiently and effectively than using either method alone. Our approach is based on the augmentation of local search patterns with location sets generated through improvement prediction over the input space. We further develop a computational framework for asynchronous parallel implementation of the optimization algorithm. We demonstrate our methods on two standard test problems and our motivating example of calibrating a circuit device simulator. KEY WORDS: robust local optimization; improvement statistics; response surface methodology; treed Gaussian processes.
Measures of agreement between computation and experiment: Validation metrics
, 2006
"... With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, ..."
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Cited by 12 (2 self)
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With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, though valuable, are essentially qualitative. Computable measures are needed that can quantitatively compare computational and experimental results over a range of input, or control, variables to sharpen assessment of computational accuracy. This type of measure has been recently referred to as a validation metric. We discuss various features that we believe should be incorporated in a validation metric, as well as features that we believe should be excluded. We develop a new validation metric that is based on the statistical concept of confidence intervals. Using this fundamental concept, we construct two specific metrics: one that requires interpolation of experimental data and one that requires regression (curve fitting) of experimental data. We apply the metrics to three example problems: thermal decomposition of a polyurethane foam, a turbulent buoyant plume of helium, and compressibility effects on the growth rate of a turbulent freeshear layer. We discuss how the present metrics are easily interpretable for assessing computational model accuracy, as well as the impact of experimental measurement uncertainty on the accuracy assessment.
D (2006) Model error in weather and climate forecasting. In: Palmer T, Hagedorn R (eds) Predictability of weather and climate. Cambridge University Press, Cambridge Anderson JL (2001) An ensemble adjustment Kalman filter for data assimilation. Mon Weather
 Cliffs, NJ Bengtsson T, Snyder C, Nychka D
, 1999
"... “As if someone were to buy several copies of the morning newspaper to assure himself that what it said was true ” Ludwig Wittgenstein 1 ..."
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Cited by 11 (3 self)
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“As if someone were to buy several copies of the morning newspaper to assure himself that what it said was true ” Ludwig Wittgenstein 1
Parameter estimation for computationally intensive nonlinear regression with an application to climate modeling
 Ann. Appl. Statist
, 2008
"... Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameterdependent nonlinear function is computationally intensive, a straightforward regression analysis by maximum likelihood is not feasible. The method presented in ..."
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Cited by 6 (0 self)
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Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameterdependent nonlinear function is computationally intensive, a straightforward regression analysis by maximum likelihood is not feasible. The method presented in this paper proposes to construct a faster running surrogate for such a computationally intensive nonlinear function, and to use it in a related nonlinear statistical model that accounts for the uncertainty associated with this surrogate. A pivotal quantity in the Earth’s climate system is the climate sensitivity: the change in global temperature due to doubling of atmospheric CO2 concentrations. This, along with other climate parameters, are estimated by applying the statistical method developed in this paper, where the computationally intensive nonlinear function is the MIT 2D climate model. 1. Introduction. A fundamental question in understanding the Earth’s
HIERARCHICAL NONLINEAR APPROXIMATION FOR EXPERIMENTAL DESIGN AND STATISTICAL DATA FITTING
"... Abstract. This paper proposes a hierarchical nonlinear approximation scheme for scalarvalued multivariate functions, where the main objective is to obtain an accurate approximation with using only very few function evaluations. To this end, our iterative method combines at any refinement step the s ..."
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Cited by 6 (1 self)
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Abstract. This paper proposes a hierarchical nonlinear approximation scheme for scalarvalued multivariate functions, where the main objective is to obtain an accurate approximation with using only very few function evaluations. To this end, our iterative method combines at any refinement step the selection of suitable evaluation points with kriging, a standard method for statistical data analysis. Particular improvements over previous nonhierarchical methods are mainly concerning the construction of new evaluation points at run time. In this construction process, referred to as experimental design, a flexible twostage method is employed, where adaptive domain refinement is combined with sequential experimental design. The hierarchical method is applied to statistical data analysis, where the data is generated by a very complex and computationally expensive computer model, called a simulator. In this application, a fast and accurate statistical approximation, called an emulator, is required as a cheap surrogate of the expensive simulator. The construction of the emulator relies on computer experiments using a very small set of carefully selected input configurations for the simulator runs. The hierarchical method proposed in this paper is, for various analysed models from reservoir forecasting, more efficient than existing standard methods. This is supported by numerical results, which show that our hierarchical method is, at comparable computational costs, up to ten times more accurate than traditional nonhierarchical methods, as utilized in commercial software relying on the response surface methodology (RSM).
INFERRING LIKELIHOODS AND CLIMATE SYSTEM CHARACTERISTICS FROM CLIMATE MODELS AND MULTIPLE TRACERS
 SUBMITTED TO THE ANNALS OF APPLIED STATISTICS
"... An important potential outcome of anthropogenic climate change is a possible collapse of the Atlantic meridional overturning circulation (AMOC). Assessing the risk of an AMOC collapse is of considerable interest since it may result in major temperature and precipitation changes and a shift in terres ..."
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Cited by 4 (4 self)
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An important potential outcome of anthropogenic climate change is a possible collapse of the Atlantic meridional overturning circulation (AMOC). Assessing the risk of an AMOC collapse is of considerable interest since it may result in major temperature and precipitation changes and a shift in terrestrial ecosystems. One key source of uncertainty in AMOC predictions is uncertainty about background ocean vertical diffusivity (Kv), a key model parameter. Kv cannot be directly observed but can be inferred by combining climate model output with observations on the oceans (so called “tracers”). In this work, we combine information from multiple tracers, each observed on a spatial grid. Our two stage approach emulates the computationally expensive climate model using a flexible hierarchical model to connect the tracers. We then infer Kv using our emulator and the observations via a Bayesian approach, accounting for observation error and model discrepancy. We utilize kernel mixing and matrix identities in our Gaussian process model to considerably reduce the computational burdens imposed by the large data sets. We find that our approach is flexible, reduces identifiability issues, and enables inference about Kv based on large data sets. We use the resulting inference about Kv to improve probabilistic projections of the AMOC.