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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

(a) The integer Latin Hypercube (LHC) used to generate the first extension of our example eight-point LHC in two dimensions. The cyan panels highlight the new integer LHC that will be used to generate new points. (b) Dividing each solid in the identified integer LHC into km equally sized solids. One of the mini-solids that has no points along it in either dimension will be chosen at random to contain the new LHC points for each of the larger cyan solids identified by the integer LHC
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fig02: (a) The integer Latin Hypercube (LHC) used to generate the first extension of our example eight-point LHC in two dimensions. The cyan panels highlight the new integer LHC that will be used to generate new points. (b) Dividing each solid in the identified integer LHC into km equally sized solids. One of the mini-solids that has no points along it in either dimension will be chosen at random to contain the new LHC points for each of the larger cyan solids identified by the integer LHC

Mentions: Our goal is to end up with a kn-point LHC comprising kn-point LHCs, so we require a further k − 1 extensions to this LHC. For the first extension, we choose another integer LHC so that both, it and the 2n × m matrix of integers, formed by stacking the two integer LHCs row-wise meets our criteria described in Section 6. This second integer LHC identifies the m-dimensional rectangular solids in which the new points will reside, as depicted for our ongoing example in Figure 2(a). We now divide each of the identified solids into km equally sized solids by dividing the range of each input within that solid into k identically sized bins, as shown in Figure 2(b).


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

Williamson D - Environmetrics (2015)

(a) The integer Latin Hypercube (LHC) used to generate the first extension of our example eight-point LHC in two dimensions. The cyan panels highlight the new integer LHC that will be used to generate new points. (b) Dividing each solid in the identified integer LHC into km equally sized solids. One of the mini-solids that has no points along it in either dimension will be chosen at random to contain the new LHC points for each of the larger cyan solids identified by the integer LHC
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig02: (a) The integer Latin Hypercube (LHC) used to generate the first extension of our example eight-point LHC in two dimensions. The cyan panels highlight the new integer LHC that will be used to generate new points. (b) Dividing each solid in the identified integer LHC into km equally sized solids. One of the mini-solids that has no points along it in either dimension will be chosen at random to contain the new LHC points for each of the larger cyan solids identified by the integer LHC
Mentions: Our goal is to end up with a kn-point LHC comprising kn-point LHCs, so we require a further k − 1 extensions to this LHC. For the first extension, we choose another integer LHC so that both, it and the 2n × m matrix of integers, formed by stacking the two integer LHCs row-wise meets our criteria described in Section 6. This second integer LHC identifies the m-dimensional rectangular solids in which the new points will reside, as depicted for our ongoing example in Figure 2(a). We now divide each of the identified solids into km equally sized solids by dividing the range of each input within that solid into k identically sized bins, as shown in Figure 2(b).

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