Bayesian Copulae Distributions, with Application to Operational Risk Management

The aim of this paper is to introduce a new methodology for operational risk management, based on Bayesian copulae. One of the main problems related to operational risk management is understanding the complex dependence structure of the associated variables. In order to model this structure in a flexible way, we construct a method based on copulae. This allows us to split the joint multivariate probability distribution of a random vector of losses into individual components characterized by univariate marginals. Thus, copula functions embody all the information about the correlation between variables and provide a useful technique for modelling the dependency of a high number of marginals. Another important problem in operational risk modelling is the lack of loss data. This suggests the use of Bayesian models, computed via simulation methods and, in particular, Markov chain Monte Carlo. We propose a new methodology for modelling operational risk and for estimating the required capital. This methodology combines the use of copulae and Bayesian models.      

Proposal for an Invariant Nonlinear Eddy Viscosity Model based on a Consistent 4D Turbulence Modelling Approach

The aim of this new approach is to demonstrate that modelling on a 3D spatial manifold is not equivalent to modelling on a true 4D space-time manifold within Newtonian physics. In the framework of turbulence modelling it will be shown that by geometrically reformulating the averaged Navier-Stokes equations on a 4D non-Riemannian manifold without changing the physical content of the theory, additional modelling restrictions will naturally emerge which are absent in the usual Euclidean (3 + 1)D formulation. By proposing a non-linear eddy viscosity model within the k − ϵ family for high turbulent Reynolds numbers the new invariant modelling approach will demonstrate its clear superiority over current (3 + 1)D modelling techniques. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and analysis of a non-regular electronic circuit via a variational inequality formulation

In this paper, we present a new and alternative mathematical modelling and analysis methodology for a class of non-regular electronic circuits through a rectifier-stabilizer circuit using the superpotentiel of Moreau and the theory of variational inequalities. This methodology is suitable for engineers to study a large class of applications.     

New advances in economic modelling and evaluation of environmental issues

This paper gives an overview of recent progress made in modelling economic environmental systems and in environmental policy analysis. In the modelling part attention will be given to new integrating frameworks offered inter alia by materials balance approaches, especially in the context of linkages between physical environmental phenomena and economic production and valuation. These can be relevant for studying materials-product chains, multisectoral materials flows, or even multiple use of complex ecosystems. Modern approaches will be dealt with, such as analysis for sustainable development, and ways of incorporating scenario experiments in environmental modelling approaches. In the context of sustainable development, modelling of multiple use of ecosystems and of spatial dimensions is also discussed. In the last part of the paper new advances in the area of environmental policy analysis will be dealt with. The main focus will be on methods for addressing uncertainty in evaluating environmental policy strategies, in particular fuzzy information and the use of meta-analysis.     

Forecasting S-shaped diffusion processes via response modelling methodology

Diffusion processes abound in various areas of corporate activities, such as the time-dependent behaviour of cumulative demand of a new product, or the adoption rate of a technological innovation. In most cases, the proportion of the population that has adopted the new product by time t behaves like an S-shaped curve, which resembles the sigmoid curve typical to many known statistical distribution functions. This analogy has motivated the common use of the latter for forecasting purposes. Recently, a new methodology for empirical modelling has been developed, termed response modelling methodology (RMM). The error distribution of the RMM model has been shown to model well variously shaped distribution functions, and may therefore be adequate to forecast sigmoid-curve processes. In particular, RMM may be applied to forecast S-shaped diffusion processes. In this paper, forty-seven data sets, assembled from published sources by Meade and Islam, are used to compare the accuracy and the stability of RMM-generated forecasts, relative to current commonly applied models. Results show that in most comparisons RMM forecasts outperform those based on any individually selected distributional model.     

Chartwell Books: A Case Study in Mathematical Modelling

A case is described that has been used successfully many times as a vehicle for teaching mathematical modelling. The case has been closely derived from a consultancy assignment with Chartwell Books. The place of mathematical modelling within decision-support systems is examined, and this is followed by an outline of one such mathematical modelling methodology. The problem situation facing the managing director of Chartwell Books concerning the modelling of labour and material costs is described. A detailed application of the mathematical modelling methodology is worked through, finishing with a discussion of the value of the case for student teaching and of the problems that students have encountered when tackling the Chartwell case. Possible extensions to the basic methodology, such as validation and the human-computer interface, are also briefly considered.     

Modelling impacts of cropping systems: Demands and solutions for DEX methodology

Decision modelling of diverse groups of problems makes different requirements to the modelling methodologies and software. We present an actual decision problem and the required characteristics of corresponding decision models. The problem is from agronomy and addresses the ecological and economic impacts of cropping systems, with the focus on the differences between cropping systems with conventional crops and the ones with genetically modified crops. We describe the extensions of an existing DEX qualitative multi-attribute modelling methodology, which were made to cope with the challenges of the problem. The extensions address general hierarchical structures, probabilistic utility functions and numerical values of basic attributes. A new, freely available software tool called proDEX was implemented to support the extended methodology. In this paper we describe the problem of cropping system assessment, propose methodological extensions to DEX, and present the implementation of proDEX.     

Encapsulating Formal Methods within Domain Specific Languages: A Solution for Verifying Railway Scheme Plans

The development and application of formal methods is a long standing research topic within the field of computer science. One particular challenge that remains is the uptake of formal methods into industrial practices. This paper introduces a methodology for developing domain specific languages for modelling and verification to aid in the uptake of formal methods within industry. It illustrates the successful application of this methodology within the railway domain. The presented methodology addresses issues surrounding faithful modelling, scalability of verification and accessibility to modelling and verification processes for practitioners within the domain.     

Maturity,distance and density (MD<Superscript>2</Superscript>) metrics for optimizing trust prediction for business intelligence

The modelling and management of trust between interacting parties are crucial parts of the overall business intelligence strategy for any organization. Predicting trust values is a key element of modelling and managing trust. It is of critical importance when the interaction is to be conducted at a future point in time. In the existing body of work, there are a few approaches for predicting trust. However, none of these approaches proposes a framework or methodology by which the predicted trust value can be considered in light of its accuracy or confidence level. This is a key element in order to ensure optimized trust prediction. In this paper, we propose a methodology to address this critical issue. The methodology comprises a suite of metrics—maturity, distance and density (MD²) which are capable of capturing various aspects of the confidence level in the predicted trust value. The proposed methodology is exemplified with the help of case studies.     

A modelling framework for comparative testing of energy forecasts

A project is described in which a methodology was developed for the comparative testing of medium-term national energy forecasts. The basis of the approach is a computer modelling system which can be used flexibly to investigate the dynamics of alternative assumptions about energy futures. The application of the methodology to the forecasts produced by a particular research group is discussed and the educative value of a modelling approach for the users in this case is explained. The study is intended as a contribution to the U.K. national debate on energy policy.     

Multicriteria evidential reasoning decision modelling and analysis—prioritizing voices of customer

In this paper, a new methodology is investigated to support the prioritization of the voices of customers through various customer satisfaction surveys. This new methodology consists of two key components: an innovative evidence-driven decision modelling framework for representing and transforming large amounts of data sets and a generic reasoning-based decision support process for aggregating evidence to prioritize the voices of customer on the basis of the Evidential Reasoning (ER) approach. Methods and frameworks for data collection and representation via multiple customer satisfaction surveys were examined first and the distinctive features of quantitative and qualitative survey data are analysed. Several novel yet natural and pragmatic rule-based functions are then proposed to transform survey data systematically and consistently from different measurement scales to a common scale, with the original features and profiles of the data preserved in the transformation process. These new transformation functions are proposed to mimic expert judgement processes and designed to be sufficiently flexible and rigorous so that expert judgements and domain specific knowledge can be taken into account naturally, systematically and consistently in the transformation process. The ER approach is used for synthesizing quantitative and qualitative data under uncertainty that can be caused due to missing data and ambiguous survey questions. A new generic method is also proposed for ranking the voices of customer based on qualitative measurement scales without having to quantify assessment grades to fixed numerical values. A case study is examined using an Intelligent Decision System (IDS) to illustrate the application of the decision modelling framework and decision support process for prioritizing the voices of customer for a world-leading car manufacturer.     

Application of A.I. techniques to formulation in mathematical modelling

The International Conference on the Teaching of Mathematical Modelling held at Exeter University, England in 1983 highlighted the need and necessity for establishing a methodology in mathematical modelling. Central to this aim is the need for a deeper understanding of the cognitive aspects of the formulation stage of the modelling process. This paper describes a major project currently under way at the Polytechnic of the South Bank in London.The project aims to build interpretation models at the object and meta-levels and to refine these models from empirical data gathered from experts. This technique is being developed for commercial expert systems technology and the author believes that this approach will provide valuable insight into the processes involved in formulation.     

An architecture for knowledge evolution in organisations

Methodology for Knowledge System Management (MKSM) is a methodology, based on modelling techniques, to support knowledge capitalisation and management. This kind of approach faces a new challenge: knowledge evolution. Indeed, as knowledge of the organisation evolves, it seems necessary to have models and supporting tools to represent this evolution. Biologic evolution theories can offer the basis of a dynamic theory of Knowledge System evolution. We especially propose to adapt Lamarckism's principles and the Cladistic classification to support such a modelling and propose a conceptual architecture for managing knowledge evolution.     

Automated generation of LFT-based parametric uncertainty descriptions from generic aircraft models

A computer assisted modelling methodology is developed for the generation of linearized models with parametric uncertainties described by Linear Fractional Transformations (LFTs). The starting point of the uncertainty modelling is a class of generic nonlinear aircraft models with explicit parametric dependence used for simulation purposes. The proposed methodology integrates specialized software tools for object-oriented modelling, for simulation, and for numerical as well as symbolic computations. The methodology has many generic features being applicable to similar nonlinear model classes.     

Dynamic modelling and performance study of solar gas tunnel dryer

The work presented in this article focuses on the analysis and modelling of heat and mass transfers in the tunnel dryer during the drying of agricultural products. The main objective of this work is to establish a global modelling of the studied system based on the bond graph methodology. The pseudo-bond graph methodology was used in modelling the system. Such methodology was very suitable for this thermal process since it allows good management of the nonlinearity present in the system.

The thermal performance of the proposed dryer is analysed by solving the various energy balance equations. An application of drying tomatoes was achieved and a fair agreement was observed between predicted and experimental results.     

Maintenance models based on the <Emphasis Type="Italic">np</Emphasis> control charts with respect to the sampling interval

This paper develops models for the maintenance of a system based on np control charts with respect to the sampling interval. At any given time, the system is assumed to be in one of the three possible states; in-control, out-of-control and failure. If the control chart signals, suggesting the possibility of an out-of-control state, an investigation will be carried out. We assume that this investigation is perfect in that it reveals the true state of the system. If an assignable cause is confirmed by the investigation, a minor repair will be carried out to remove the cause. If the assignable cause is not attended to, it will gradually develop into a failure. When a failure occurs, the system cannot operate and a major repair is needed. We discuss three models depending on the assumptions related to the renewal mechanism, the occurrence of failures, and the time between minor repairs. The paper seeks to optimise the performance of such a system in terms of the sampling interval. Geometric processes are utilised for modelling the lifetimes between minor repairs if the minor repair cannot bring the system back to an as good as new condition. The expected cost per unit time for maintaining the systems with respect to the sampling interval of the control chart is obtained. Numerical examples are conducted to demonstrate the applicability of the methodology derived.     

Shape-matching and classification using structural descriptors

Technological improvements related to object acquisition, visualisation and modelling, have caused a considerable growth of the number of 3D models in digital form. Digital 3D models are now available in large databases of shapes, ranging from unstructured repositories, like the web, to specialised catalogues used in engineering and simulation. In this panorama it is clear that methods for the retrieval and automatic classification of 3D content will play a crucial role in the development of efficient applications for the organisation and filtering of 3D data. In this paper, a methodology based on the coupling of geometric and structural information will be discussed for the global and partial matching of 3D shapes and for their automatic classification. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uncertainty quantification for functional dependent random variables

This paper proposes a new methodology to model uncertainties associated with functional random variables. This methodology allows to deal simultaneously with several dependent functional variables and to address the specific case where these variables are linked to a vectorial variable, called covariate. In this case, the proposed uncertainty modelling methodology has two objectives: to retain both the most important features of the functional variables and their features which are the most correlated to the covariate. This methodology is composed of two steps. First, the functional variables are decomposed on a functional basis. To deal simultaneously with several dependent functional variables, a Simultaneous Partial Least Squares algorithm is proposed to estimate this basis. Second, the joint probability density function of the coefficients selected in the decomposition is modelled by a Gaussian mixture model. A new sparse method based on a Lasso penalization algorithm is proposed to estimate the Gaussian mixture model parameters and reduce their number. Several criteria are introduced to assess the methodology performance: its ability to approximate the functional variables probability distribution, their dependence structure and their features which explain the covariate. Finally, the whole methodology is applied on a simulated example and on a nuclear reliability test case.     

Value at risk methodology under soft conditions approach (fuzzy-stochastic approach)

The paper describes methodology of dealing with financial modelling under uncertainty with risk and vagueness aspects. An approach to modelling risks by the Value at Risk methodology under imprecise and soft conditions is solved. It is supposed that the input data and problem conditions is difficult to determine as real numbers or as some precise distribution function. Thus, vagueness is modelled through the fuzzy numbers of the linear T-number type. The combination of risk and vagueness is solved by fuzzy-stochastic methodology. Illustrative example is introduced.