(2009) 'Small sample Bayesian designs for complex high-dimensional models based on information gained using fast approximations. ', Technometrics., 51 (4 Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe consider the problem of designing for complex high-dimensional computer models which can be evaluated at different levels of accuracy. Ordinarily, this requires performing many expensive evaluations of the most accurate version of the computer model in order to obtain a reasonable coverage of the design space. In some cases, it is possible to supplement the information from the accurate model evaluations with a large number of evaluations of a cheap, approximate version of the computer model to enable a more informed design choice. We describe an approach which combines the information from both the approximate model and the accurate model into a single multiscale emulator for the computer model. We then propose a design strategy for the selection of a small number of expensive evaluations of the accurate computer model based on our multiscale emulator and a decomposition of the input parameter space. The methodology is illustrated with an example concerning a computer simulation of a hydrocarbon reservoir.

Computer models are now widely used across a range of scientific disciplines to describe various complex physical systems, however to perform full uncertainty quantification we often need to employ emulators. An emulator is a fast statistical construct that mimics the complex computer model, and greatly aids the vastly more computationally intensive uncertainty quantification calculations that a serious scientific analysis often requires. In some cases, the complex model can be solved far more efficiently for certain parameter settings, leading to boundaries or hyperplanes in the input parameter space where the model is essentially known. We show that for a large class of Gaussian process style emulators, multiple boundaries can be formally incorporated into the emulation process, by Bayesian updating of the emulators with respect to the boundaries, for trivial computational cost. The resulting updated emulator equations are given analytically. This leads to emulators that possess increased accuracy across large portions of the input parameter space. We also describe how a user can incorporate such boundaries within standard black box GP emulation packages that are currently available, without altering the core code. Appropriate designs of model runs in the presence of known boundaries are then analysed, with two kinds of general purpose designs proposed. We then apply the improved emulation and design methodology to an important systems biology model of hormonal crosstalk in Arabidopsis Thaliana.

. (2007) Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractFor many large-scale data sets it is necessary to reduce dimensionality to the point where further exploration and analysis can take place. Principal variables are a subset of the original variables and preserve, to some extent, the structure and information carried by the original variables. Dimension reduction using principal variables is considered and a novel algorithm for determining such principal variables is proposed. This method is tested and compared with eleven other variable selection methods from the literature in a simulation study and is shown to be highly effective. Extensions to this procedure are also developed, including a method to determine longitudinal principal variables for repeated measures data, and a technique for incorporating utilities in order to modify the selection process. The method is further illustrated with real data sets, including some larger UK data relating to patient outcome after total knee replacement.

A statistical method to determine the number of measurements required from nanomaterials to ensure reliable and robust analysis is described. Commercial products utilizing graphene are in their infancy and recent investigations of commercial graphene manufacture have attributed this to the lack of robust metrology and standards by which graphene and related carbon materials can be measured and compared. Raman spectroscopy is known to be a useful tool in carbon nanomaterial characterization, but to provide meaningful information, in particular for quality control or management, multiple spectra are needed. Herein we present a statistical method to quantify the number of different spectra or other microscale measurements that should be taken to reliably characterize a graphene material. We have recorded a large number of Raman measurements and studied the statistical convergence of these data sets. We use a graphical approach to monitor the change in summary statistics and a Monte Carlo based bootstrapping method of data analysis to computationally resample the data demonstrating the effects of underanalyzing a material; for example, graphene nanoplatelets may require over 500 spectra before information about the exfoliation efficiency, particle size, layer number, and chemical functionalization is accurately obtained.

Uncertainty in well test analysis results from errors in pressure and rate measurements, from uncertainties in basic well and reservoir parameters; from the quality of the match with the interpretation model; and from the non-uniqueness of the interpretation model. These various uncertainties, except the non-uniqueness of the interpretation model, were examined in SPE 113888. It was concluded that the permeability-product kh is generally known within 15%; the permeability k, within 20% (because of the uncertainty on the thickness h); and the skin effect S, within 8% for high S values and within ±0.5 for low S values. Distances (half-fracture lengths, horizontal well lengths, and distances to reservoir boundaries) are usually known within 25%. The issue of non-uniqueness of the interpretation model is more complex: not only may there be a multitude of possible models for any one derivative response (the usual inverse problem), but there may be also a multitude of derivative responses, due to the uncertainty inherent in the observed data. This paper presents a methodology for assessing the derivative response uncertainty using deconvolution. It is shown that the uncertainty depends mainly on the error bounds for initial pressure and flow rates, which yield a range of possible shapes for the deconvolved pressure derivative and therefore different possible interpretation models. In some cases, the non-uniqueness of deconvolution can be reduced using knowledge of the expected model response, for instance from geology or seismic. In the absence of differentiating information, however, alternative interpretation models have to be considered, which may lead to completely different development options. The methodology is illustrated with three field examples.