Limits...
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

Leave One Latin Hypercube Out plots against a coefficient controlling vertical eddies, for each of the 25 16-member sub-Latin Hypercubes that made up our ocean model design.
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fig08: Leave One Latin Hypercube Out plots against a coefficient controlling vertical eddies, for each of the 25 16-member sub-Latin Hypercubes that made up our ocean model design.

Mentions: The plots indicate that the emulator represents the model well. The prediction intervals are approximately 95% so we should expect around 20 points not to be within the uncertainty bounds, and we see 18. Additionally, we would be concerned if any of the red points were very far from the error bars, indicating a mis-specification of the variance across parameter space. We do not see any such points. Although these are useful plots, the LOLHO plots we present in Figures 7 and 8 offer further diagnostic insight. Each panel represents a left out LHC where at this time, the entire LHC is left out and all points predicted with the refitted emulator. Figure 7 plots each left out LHC against the Langmuir cells coefficient in the vertical mixing scheme, and Figure 8 plots each LHC against a coefficient controlling the vertical behaviour of eddies. In both figures, from the left, the first four panels depict LOLHO plots for the four hypercubes with the switch exclusively in its first setting, the next four in its second setting, and the remaining panels represent a balanced design in the switches.


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

Williamson D - Environmetrics (2015)

Leave One Latin Hypercube Out plots against a coefficient controlling vertical eddies, for each of the 25 16-member sub-Latin Hypercubes that made up our ocean model design.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig08: Leave One Latin Hypercube Out plots against a coefficient controlling vertical eddies, for each of the 25 16-member sub-Latin Hypercubes that made up our ocean model design.
Mentions: The plots indicate that the emulator represents the model well. The prediction intervals are approximately 95% so we should expect around 20 points not to be within the uncertainty bounds, and we see 18. Additionally, we would be concerned if any of the red points were very far from the error bars, indicating a mis-specification of the variance across parameter space. We do not see any such points. Although these are useful plots, the LOLHO plots we present in Figures 7 and 8 offer further diagnostic insight. Each panel represents a left out LHC where at this time, the entire LHC is left out and all points predicted with the refitted emulator. Figure 7 plots each left out LHC against the Langmuir cells coefficient in the vertical mixing scheme, and Figure 8 plots each LHC against a coefficient controlling the vertical behaviour of eddies. In both figures, from the left, the first four panels depict LOLHO plots for the four hypercubes with the switch exclusively in its first setting, the next four in its second setting, and the remaining panels represent a balanced design in the switches.

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