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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 first three 8-point Latin Hypercubes (LHCs) generated during application of the extension algorithm with different coloured grid squares representing the three integer LHCs used to identify the regions of the new points. (b) The full 40 point LHC comprising five 8-point LHCs. The integer LHCs used to generate each extension are highlighted as different coloured grid squares.
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fig03: (a) The first three 8-point Latin Hypercubes (LHCs) generated during application of the extension algorithm with different coloured grid squares representing the three integer LHCs used to identify the regions of the new points. (b) The full 40 point LHC comprising five 8-point LHCs. The integer LHCs used to generate each extension are highlighted as different coloured grid squares.

Mentions: We now repeat this process a further (k − 2) times. First is choosing an n-point integer LHC with desirable properties when combined with all other integer LHCs used in the design, then dividing each identified solid into km identically sized solids before looking along each dimension of the design through each sub-solid in order to identify all sub-solids with no visible points along any dimensions. When adding the j-th additional n-member LHC to the original X, there will be (k − j)m such solids from which a sub-solid may be selected at random and a design point selected uniformly from within. This is shown for a five-extended LHC of dimension 2 and size 40 in Figure 3. Figure 3(a) shows the process after two extensions with the three chosen integer LHCs highlighting the selected solids coloured in red, cyan and yellow, and the chosen points in black. Note that along any of the sub-rows/columns, there is a maximum of one point. When the final extension occurs, exactly one sub-solid in each identified solid will be eligible for a new point, and following its placement and addition of all points into X, every one of the kn equally sized sub-intervals of each dimension of will be represented exactly once in X. So X is a kn LHC composed of kn-point LHCs where the whole and the sequentially generated sub-designs have been engineered to have desirable properties. This is depicted for our on-going example in Figure 3(b).


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

Williamson D - Environmetrics (2015)

(a) The first three 8-point Latin Hypercubes (LHCs) generated during application of the extension algorithm with different coloured grid squares representing the three integer LHCs used to identify the regions of the new points. (b) The full 40 point LHC comprising five 8-point LHCs. The integer LHCs used to generate each extension are highlighted as different coloured grid squares.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig03: (a) The first three 8-point Latin Hypercubes (LHCs) generated during application of the extension algorithm with different coloured grid squares representing the three integer LHCs used to identify the regions of the new points. (b) The full 40 point LHC comprising five 8-point LHCs. The integer LHCs used to generate each extension are highlighted as different coloured grid squares.
Mentions: We now repeat this process a further (k − 2) times. First is choosing an n-point integer LHC with desirable properties when combined with all other integer LHCs used in the design, then dividing each identified solid into km identically sized solids before looking along each dimension of the design through each sub-solid in order to identify all sub-solids with no visible points along any dimensions. When adding the j-th additional n-member LHC to the original X, there will be (k − j)m such solids from which a sub-solid may be selected at random and a design point selected uniformly from within. This is shown for a five-extended LHC of dimension 2 and size 40 in Figure 3. Figure 3(a) shows the process after two extensions with the three chosen integer LHCs highlighting the selected solids coloured in red, cyan and yellow, and the chosen points in black. Note that along any of the sub-rows/columns, there is a maximum of one point. When the final extension occurs, exactly one sub-solid in each identified solid will be eligible for a new point, and following its placement and addition of all points into X, every one of the kn equally sized sub-intervals of each dimension of will be represented exactly once in X. So X is a kn LHC composed of kn-point LHCs where the whole and the sequentially generated sub-designs have been engineered to have desirable properties. This is depicted for our on-going example in Figure 3(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