Managing uncertainty in complex stochastic models: design and emulation of a Rabies model

In this paper we present a novel method for emulating a stochastic, or random output, computer model and show its application to a complex rabies model. The method is evaluated both in terms of accuracy and computational efficiency on synthetic data and the rabies model. We address the issue of experimental design and provide empirical evidence on the effectiveness of utilizing replicate model evaluations compared to a space-filling design. We employ the Mahalanobis error measure to validate the heteroscedastic Gaussian process based emulator predictions for both the mean and (co)variance. The emulator allows efficient screening to identify important model inputs and better understanding of the complex behaviour of the rabies model.

Theory and data for area summation of contrast with and without uncertainty:evidence for a noisy energy model

Contrast sensitivity improves with the area of a sine-wave grating, but why? Here we assess this phenomenon against contemporary models involving spatial summation, probability summation, uncertainty, and stochastic noise. Using a two-interval forced-choice procedure we measured contrast sensitivity for circular patches of sine-wave gratings with various diameters that were blocked or interleaved across trials to produce low and high extrinsic uncertainty, respectively. Summation curves were steep initially, becoming shallower thereafter. For the smaller stimuli, sensitivity was slightly worse for the interleaved design than for the blocked design. Neither area nor blocking affected the slope of the psychometric function. We derived model predictions for noisy mechanisms and extrinsic uncertainty that was either low or high. The contrast transducer was either linear (c1.0) or nonlinear (c2.0), and pooling was either linear or a MAX operation. There was either no intrinsic uncertainty, or it was fixed or proportional to stimulus size. Of these 10 canonical models, only the nonlinear transducer with linear pooling (the noisy energy model) described the main forms of the data for both experimental designs. We also show how a cross-correlator can be modified to fit our results and provide a contemporary presentation of the relation between summation and the slope of the psychometric function.

Uncertainty analysis in the Model Web

This thesis provides a set of tools for managing uncertainty in Web-based models and workflows.To support the use of these tools, this thesis firstly provides a framework for exposing models through Web services. An introduction to uncertainty management, Web service interfaces,and workflow standards and technologies is given, with a particular focus on the geospatial domain.An existing specification for exposing geospatial models and processes, theWeb Processing Service (WPS), is critically reviewed. A processing service framework is presented as a solutionto usability issues with the WPS standard. The framework implements support for Simple ObjectAccess Protocol (SOAP), Web Service Description Language (WSDL) and JavaScript Object Notation (JSON), allowing models to be consumed by a variety of tools and software. Strategies for communicating with models from Web service interfaces are discussed, demonstrating the difficultly of exposing existing models on the Web. This thesis then reviews existing mechanisms for uncertainty management, with an emphasis on emulator methods for building efficient statistical surrogate models. A tool is developed to solve accessibility issues with such methods, by providing a Web-based user interface and backend to ease the process of building and integrating emulators. These tools, plus the processing service framework, are applied to a real case study as part of the UncertWeb project. The usability of the framework is proved with the implementation of aWeb-based workflow for predicting future crop yields in the UK, also demonstrating the abilities of the tools for emulator building and integration. Future directions for the development of the tools are discussed.

Uncertainty propagation in the model web:a case study with e-Habitat

eHabitat is a Web Processing Service (WPS) designed to compute the likelihood of finding ecosystems with equal properties. Inputs to the WPS, typically thematic geospatial "layers", can be discovered using standardised catalogues, and the outputs tailored to specific end user needs. Because these layers can range from geophysical data captured through remote sensing to socio-economical indicators, eHabitat is exposed to a broad range of different types and levels of uncertainties. Potentially chained to other services to perform ecological forecasting, for example, eHabitat would be an additional component further propagating uncertainties from a potentially long chain of model services. This integration of complex resources increases the challenges in dealing with uncertainty. For such a system, as envisaged by initiatives such as the "Model Web" from the Group on Earth Observations, to be used for policy or decision making, users must be provided with information on the quality of the outputs since all system components will be subject to uncertainty. UncertWeb will create the Uncertainty-Enabled Model Web by promoting interoperability between data and models with quantified uncertainty, building on existing open, international standards. It is the objective of this paper to illustrate a few key ideas behind UncertWeb using eHabitat to discuss the main types of uncertainties the WPS has to deal with and to present the benefits of the use of the UncertWeb framework.

The uncertainty enabled model web (UncertWeb)

UncertWeb is a European research project running from 2010-2013 that will realize the uncertainty enabled model web. The assumption is that data services, in order to be useful, need to provide information about the accuracy or uncertainty of the data in a machine-readable form. Models taking these data as imput should understand this and propagate errors through model computations, and quantify and communicate errors or uncertainties generated by the model approximations. The project will develop technology to realize this and provide demonstration case studies.

Management interventions in dairy herds: exploring within herd uncertainty using an integrated Bayesian model

Knowledge of the efficacy of an intervention for disease control on an individual farm is essential to make good decisions on preventive healthcare, but the uncertainty in outcome associated with undertaking a specific control strategy has rarely been considered in veterinary medicine. The purpose of this research was to explore the uncertainty in change in disease incidence and financial benefit that could occur on different farms, when two effective farm management interventions are undertaken. Bovine mastitis was used as an example disease and the research was conducted using data from an intervention study as prior information within an integrated Bayesian simulation model. Predictions were made of the reduction in clinical mastitis within 30 days of calving on 52 farms, attributable to the application of two herd interventions previously reported as effective; rotation of dry cow pasture and differential dry cow therapy. Results indicated that there were important degrees of uncertainty in the predicted reduction in clinical mastitis for individual farms when either intervention was undertaken; the magnitude of the 95% credible intervals for reduced clinical mastitis incidence were substantial and of clinical relevance. The large uncertainty associated with the predicted reduction in clinical mastitis attributable to the interventions resulted in important variability in possible financial outcomes for each farm. The uncertainty in outcome associated with farm control measures illustrates the difficulty facing a veterinary clinician when making an on-farm decision and highlights the importance of iterative herd health procedures (continual evaluation, reassessment and adjusted interventions) to optimise health in an individual herd.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

Leaf area index estimation with MODIS reflectance time series and model inversion during full rotations of Eucalyptus plantations

The leaf area index (LAI) of fast-growing Eucalyptus plantations is highly dynamic both seasonally and interannually, and is spatially variable depending on pedo-climatic conditions. LAI is very important in determining the carbon and water balance of a stand, but is difficult to measure during a complete stand rotation and at large scales. Remote-sensing methods allowing the retrieval of LAI time series with accuracy and precision are therefore necessary. Here, we tested two methods for LAI estimation from MODIS 250m resolution red and near-infrared (NIR) reflectance time series. The first method involved the inversion of a coupled model of leaf reflectance and transmittance (PROSPECT4), soil reflectance (SOILSPECT) and canopy radiative transfer (4SAIL2). Model parameters other than the LAI were either fixed to measured constant values, or allowed to vary seasonally and/or with stand age according to trends observed in field measurements. The LAI was assumed to vary throughout the rotation following a series of alternately increasing and decreasing sigmoid curves. The parameters of each sigmoid curve that allowed the best fit of simulated canopy reflectance to MODIS red and NIR reflectance data were obtained by minimization techniques. The second method was based on a linear relationship between the LAI and values of the GEneralized Soil Adjusted Vegetation Index (GESAVI), which was calibrated using destructive LAI measurements made at two seasons, on Eucalyptus stands of different ages and productivity levels. The ability of each approach to reproduce field-measured LAI values was assessed, and uncertainty on results and parameter sensitivities were examined. Both methods offered a good fit between measured and estimated LAI (R(2) = 0.80 and R(2) = 0.62 for model inversion and GESAVI-based methods, respectively), but the GESAVI-based method overestimated the LAI at young ages. (C) 2010 Elsevier Inc. All rights reserved.

Production under uncertainty and choice under uncertainty in the emergence of generalized expected utility theory

This paper presents a personal view of the interaction between the analysis of choice under uncertainty and the analysis of production under uncertainty. Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under uncertainty. This interest led to the development of generalized models including rank-dependent expected utility theory. In turn, the development of generalized expected utility models raised the question of whether such models could be used in the analysis of applied problems such as those involving production under uncertainty. Finally, the revival of the state-contingent approach led to the recognition of a fundamental duality between choice problems and production problems.

Characterizing QALYs under a general rank dependent utility model

This paper provides a characterization of QALYs, the most important outcome measure in medical decision making, in the context of a general rank dependent utility model. We show that both for chronic and for nonchronic health states the characterization of QALYs depends on intuitive conditions. This facilitates the assessment of the validity of QALYs in rank dependent non-expected utility theories and a comparison with other utility based measures of health.

Model-based procedure for scale-up of wet, overflow ball mills - Part III: Validation and discussion

A new ball mill scale-up procedure is developed. This procedure has been validated using seven sets of Ml-scale ball mil data. The largest ball mills in these data have diameters (inside liners) of 6.58m. The procedure can predict the 80% passing size of the circuit product to within +/-6% of the measured value, with a precision of +/-11% (one standard deviation); the re-circulating load to within +/-33% of the mass-balanced value (this error margin is within the uncertainty associated with the determination of the re-circulating load); and the mill power to within +/-5% of the measured value. This procedure is applicable for the design of ball mills which are preceded by autogenous (AG) mills, semi-autogenous (SAG) mills, crushers and flotation circuits. The new procedure is more precise and more accurate than Bond's method for ball mill scale-up. This procedure contains no efficiency correction which relates to the mill diameter. This suggests that, within the range of mill diameter studied, milling efficiency does not vary with mill diameter. This is in contrast with Bond's equation-Bond claimed that milling efficiency increases with mill diameter. (C) 2001 Elsevier Science Ltd. All rights reserved.

Methodologies for calibration and predictive analysis of a watershed model

The use of a fitted parameter watershed model to address water quantity and quality management issues requires that it be calibrated under a wide range of hydrologic conditions. However, rarely does model calibration result in a unique parameter set. Parameter nonuniqueness can lead to predictive nonuniqueness. The extent of model predictive uncertainty should be investigated if management decisions are to be based on model projections. Using models built for four neighboring watersheds in the Neuse River Basin of North Carolina, the application of the automated parameter optimization software PEST in conjunction with the Hydrologic Simulation Program Fortran (HSPF) is demonstrated. Parameter nonuniqueness is illustrated, and a method is presented for calculating many different sets of parameters, all of which acceptably calibrate a watershed model. A regularization methodology is discussed in which models for similar watersheds can be calibrated simultaneously. Using this method, parameter differences between watershed models can be minimized while maintaining fit between model outputs and field observations. In recognition of the fact that parameter nonuniqueness and predictive uncertainty are inherent to the modeling process, PEST's nonlinear predictive analysis functionality is then used to explore the extent of model predictive uncertainty.

Conceptual model for decomposing the value for the customer

Value has been defined in different theoretical contexts as need, desire, interest, standard /criteria, beliefs, attitudes, and preferences. The creation of value is key to any business, and any business activity is about exchanging some tangible and/or intangible good or service and having its value accepted and rewarded by customers or clients, either inside the enterprise or collaborative network or outside. “Perhaps surprising then is that firms often do not know how to define value, or how to measure it” (Anderson and Narus, 1998 cited by [1]). Woodruff echoed that we need “richer customer value theory” for providing an “important tool for locking onto the critical things that managers need to know”. In addition, he emphasized, “we need customer value theory that delves deeply into customer’s world of product use in their situations” [2]. In this sense, we proposed and validated a novel “Conceptual Model for Decomposing the Value for the Customer”. To this end, we were aware that time has a direct impact on customer perceived value, and the suppliers’ and customers’ perceptions change from the pre-purchase to the post-purchase phases, causing some uncertainty and doubts.We wanted to break down value into all its components, as well as every built and used assets (both endogenous and/or exogenous perspectives). This component analysis was then transposed into a mathematical formulation using the Fuzzy Analytic Hierarchy Process (AHP), so that the uncertainty and vagueness of value perceptions could be embedded in this model that relates used and built assets in the tangible and intangible deliverable exchange among the involved parties, with their actual value perceptions.

A model updating technique based on FRFs for damped structures

Model updating methods often neglect that in fact all physical structures are damped. Such simplification relies on the structural modelling approach, although it compromises the accuracy of the predictions of the structural dynamic behaviour. In the present work, the authors address the problem of finite element (FE) model updating based on measured frequency response functions (FRFs), considering damping. The proposed procedure is based upon the complex experimental data, which contains information related to the damped FE model parameters and presents the advantage of requiring no prior knowledge about the damping matrix structure or its content, only demanding the definition of the damping type. Numerical simulations are performed in order to establish the applicability of the proposed damped FE model updating technique and its results are discussed in terms of the correlation between the simulated experimental complex FRFs and the ones obtained from the updated FE model.