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.
Highlights
The use of complex mathematical models, typically in the form of coupled ordinary, partial or stochastic differential equations, to describe complex physical systems is important in many diverse scientific disciplines
We report only the details required in order to present novel emulator diagnostics based on having a k-extended Latin Hypercube design
We have presented a class of exploratory ensemble designs based on extending an algorithm for adding to existing designs first introduced by Sallaberry et al (2008) that we call kextended latin hypercubes (LHC’s)
Summary
The use of complex mathematical models, typically in the form of coupled ordinary, partial or stochastic differential equations, to describe complex physical systems is important in many diverse scientific disciplines Where these equations cannot be solved analytically and must, instead, be solved numerically using computer simulations, the developed models are referred to in the statistics literature as ‘computer models.’. The study of complex systems, such as the climate, using computer models introduces a number of sources of uncertainty that must be quantified so that appropriate inferences about the system can be made and to facilitate decision making Quantifying this uncertainty through the design and analysis of computer experiments has become an active and important avenue of statistical research, and a rich methodology for addressing typical problems exists (Santner et al, 2003). There are published statistical methodologies using emulators to assist in each of these problems (see, for example, Oakley and O’Hagan, 2004; Lee et al, 2011; Kennedy and O’Hagan, 2001; Vernon et al, 2010; Williamson and Goldstein, 2012)
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