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Exploratory ensemble designs for environmental models using k-extended Latin Hypercubes.

Williamson D - Environmetrics (2015)

Bottom Line: The resulting design and its component parts are designed so that each is approximately orthogonal and maximises a measure of coverage of the parameter space.We build an emulator for NEMO using the created design to illustrate the use of our emulator diagnostic test. © 2015 The Authors.Environmetrics published by John Wiley & Sons Ltd.

View Article: PubMed Central - PubMed

Affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter Exeter, U.K.

ABSTRACT

In this paper we present a novel, flexible, and multi-purpose class of designs for initial exploration of the parameter spaces of computer models, such as those used to study many features of the environment. The idea applies existing technology aimed at expanding a Latin Hypercube (LHC) in order to generate initial LHC designs that are composed of many smaller LHCs. The resulting design and its component parts are designed so that each is approximately orthogonal and maximises a measure of coverage of the parameter space. Designs of the type advocated for in this paper are particularly useful when we want to simultaneously quantify parametric uncertainty and any uncertainty due to the initial conditions, boundary conditions, or forcing functions required to run the model. This makes the class of designs particularly suited to environmental models, such as climate models that contain all of these features. The proposed designs are particularly suited to initial exploratory ensembles whose goal is to guide the design of further ensembles aimed at, for example, calibrating the model. We introduce a new emulator diagnostic that exploits the structure of the advocated ensemble designs and allows for the assessment of structural weaknesses in the statistical modelling. We provide illustrations of the method through a simple example and describe a 400 member ensemble of the Nucleus for European Modelling of the Ocean (NEMO) ocean model designed using the method. We build an emulator for NEMO using the created design to illustrate the use of our emulator diagnostic test. © 2015 The Authors. Environmetrics published by John Wiley & Sons Ltd.

No MeSH data available.


Related in: MedlinePlus

Traditional Leave One Out plots against the coefficient of Langmuir cells (left) and a coefficient controlling vertical eddies (right). The predictions and two standard deviation prediction intervals for the left out points are in black. The true values are in either green, if they are within two standard deviations of the prediction, or red otherwise
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fig06: Traditional Leave One Out plots against the coefficient of Langmuir cells (left) and a coefficient controlling vertical eddies (right). The predictions and two standard deviation prediction intervals for the left out points are in black. The true values are in either green, if they are within two standard deviations of the prediction, or red otherwise

Mentions: Figure 6 presents the traditional leave one out diagnostic for two of the model parameters: the Langmuir cells coefficient in the vertical mixing scheme (left panel) and a coefficient controlling the vertical behaviour of eddies (right panel). Each point represents an ensemble member that is left out of the ensemble, whilst the emulator is refitted using the same mean function and conditioned on the MAP estimates for the correlation lengths and nugget. The black points and error bars represent the emulator prediction and a two standard deviation prediction interval. The true (left out) values are then plotted in either green, if they are within two standard deviations of the prediction, or red (and larger) otherwise.


Exploratory ensemble designs for environmental models using k-extended Latin Hypercubes.

Williamson D - Environmetrics (2015)

Traditional Leave One Out plots against the coefficient of Langmuir cells (left) and a coefficient controlling vertical eddies (right). The predictions and two standard deviation prediction intervals for the left out points are in black. The true values are in either green, if they are within two standard deviations of the prediction, or red otherwise
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4440391&req=5

fig06: Traditional Leave One Out plots against the coefficient of Langmuir cells (left) and a coefficient controlling vertical eddies (right). The predictions and two standard deviation prediction intervals for the left out points are in black. The true values are in either green, if they are within two standard deviations of the prediction, or red otherwise
Mentions: Figure 6 presents the traditional leave one out diagnostic for two of the model parameters: the Langmuir cells coefficient in the vertical mixing scheme (left panel) and a coefficient controlling the vertical behaviour of eddies (right panel). Each point represents an ensemble member that is left out of the ensemble, whilst the emulator is refitted using the same mean function and conditioned on the MAP estimates for the correlation lengths and nugget. The black points and error bars represent the emulator prediction and a two standard deviation prediction interval. The true (left out) values are then plotted in either green, if they are within two standard deviations of the prediction, or red (and larger) otherwise.

Bottom Line: The resulting design and its component parts are designed so that each is approximately orthogonal and maximises a measure of coverage of the parameter space.We build an emulator for NEMO using the created design to illustrate the use of our emulator diagnostic test. © 2015 The Authors.Environmetrics published by John Wiley & Sons Ltd.

View Article: PubMed Central - PubMed

Affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter Exeter, U.K.

ABSTRACT

In this paper we present a novel, flexible, and multi-purpose class of designs for initial exploration of the parameter spaces of computer models, such as those used to study many features of the environment. The idea applies existing technology aimed at expanding a Latin Hypercube (LHC) in order to generate initial LHC designs that are composed of many smaller LHCs. The resulting design and its component parts are designed so that each is approximately orthogonal and maximises a measure of coverage of the parameter space. Designs of the type advocated for in this paper are particularly useful when we want to simultaneously quantify parametric uncertainty and any uncertainty due to the initial conditions, boundary conditions, or forcing functions required to run the model. This makes the class of designs particularly suited to environmental models, such as climate models that contain all of these features. The proposed designs are particularly suited to initial exploratory ensembles whose goal is to guide the design of further ensembles aimed at, for example, calibrating the model. We introduce a new emulator diagnostic that exploits the structure of the advocated ensemble designs and allows for the assessment of structural weaknesses in the statistical modelling. We provide illustrations of the method through a simple example and describe a 400 member ensemble of the Nucleus for European Modelling of the Ocean (NEMO) ocean model designed using the method. We build an emulator for NEMO using the created design to illustrate the use of our emulator diagnostic test. © 2015 The Authors. Environmetrics published by John Wiley & Sons Ltd.

No MeSH data available.


Related in: MedlinePlus