Adding constrained discontinuities to Gaussian process models of wind fields

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

Sparse representation for Gaussian process models

We develop an approach for a sparse representation for Gaussian Process (GP) models in order to overcome the limitations of GPs caused by large data sets. The method is based on a combination of a Bayesian online algorithm together with a sequential construction of a relevant subsample of the data which fully specifies the prediction of the model. Experimental results on toy examples and large real-world datasets indicate the efficiency of the approach.

Adding constrained discontinuities to Gaussian process models of wind fields

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

Approximately optimal experimental design for heteroscedastic Gaussian process models

This paper presents a greedy Bayesian experimental design criterion for heteroscedastic Gaussian process models. The criterion is based on the Fisher information and is optimal in the sense of minimizing parameter uncertainty for likelihood based estimators. We demonstrate the validity of the criterion under different noise regimes and present experimental results from a rabies simulator to demonstrate the effectiveness of the resulting approximately optimal designs.

GIS linked environmental process models

In recent years there has been a great effort to combine the technologies and techniques of GIS and process models. This project examines the issues of linking a standard current generation 2½d GIS with several existing model codes. The focus for the project has been the Shropshire Groundwater Scheme, which is being developed to augment flow in the River Severn during drought periods by pumping water from the Shropshire Aquifer. Previous authors have demonstrated that under certain circumstances pumping could reduce the soil moisture available for crops. This project follows earlier work at Aston in which the effects of drawdown were delineated and quantified through the development of a software package that implemented a technique which brought together the significant spatially varying parameters. This technique is repeated here, but using a standard GIS called GRASS. The GIS proved adequate for the task and the added functionality provided by the general purpose GIS - the data capture, manipulation and visualisation facilities - were of great benefit. The bulk of the project is concerned with examining the issues of the linkage of GIS and environmental process models. To this end a groundwater model (Modflow) and a soil moisture model (SWMS2D) were linked to the GIS and a crop model was implemented within the GIS. A loose-linked approach was adopted and secondary and surrogate data were used wherever possible. The implications of which relate to; justification of a loose-linked versus a closely integrated approach; how, technically, to achieve the linkage; how to reconcile the different data models used by the GIS and the process models; control of the movement of data between models of environmental subsystems, to model the total system; the advantages and disadvantages of using a current generation GIS as a medium for linking environmental process models; generation of input data, including the use of geostatistic, stochastic simulation, remote sensing, regression equations and mapped data; issues of accuracy, uncertainty and simply providing adequate data for the complex models; how such a modelling system fits into an organisational framework.

Online approximations for wind-field models

We study online approximations to Gaussian process models for spatially distributed systems. We apply our method to the prediction of wind fields over the ocean surface from scatterometer data. Our approach combines a sequential update of a Gaussian approximation to the posterior with a sparse representation that allows to treat problems with a large number of observations.

Chemical kinetic investigation of a commercial batch reactor process

The aim of this investigation was to study the chemical reactions occurring during the batchwise production of a butylated melamine-formaldehyde resin, in order to optimise the efficiency and economics of the batch processes. The batch process models are largely empirical in nature as the reaction mechanism is unknown. The process chemistry and the commercial manufacturing method are described. A small scale system was established in glass and the ability to produce laboratory resins with the required quality was demonstrated, simulating the full scale plant. During further experiments the chemical reactions of methylolation, condensation and butylation were studied. The important process stages were identified and studied separately. The effects of variation of certain process parameters on the chemical reactions were also studied. A published model of methylolation was modified and used to simulate the methylolation stage. A major result of this project was the development of an indirect method for studying the condensation and butylation reactions occurring during the dehydration and acid reaction stages, as direct quantitative methods were not available. A mass balance method was devised for this purpose and used to collect experimental data. The reaction scheme was verified using this data. The reactions stages were simulated using an empirical model. This has revealed new information regarding the mechanism and kinetics of the reactions. Laboratory results were shown to be comparable with plant scale results. This work has improved the understanding of the batch process, which can be used to improve product consistency. Future work has been identified and recommended to produce an optimum process and plant design to reduce the batch time.

Process integration and improvement using systemic diagrams and a human-centred approach

If product cycle time reduction is the mission, and the multifunctional team is the means of achieving the mission, what then is the modus operandi by which this means is to accomplish its mission? This paper asserts that a preferred modus operandi for the multifunctional team is to adopt a process-oriented view of the manufacturing enterprise, and for this it needs the medium of a process map [16] The substance of this paper is a methodology which enables the creation of such maps Specific examples of process models drawn from the product develop ment life cycle are presented and described in order to support the methodology's integrity and value The specific deliverables we have so far obtained are a methodology for process capture and analysis, a collection of process models spanning the product development cycle, and, an engineering handbook which hosts these models and presents a computer-based means of navigating through these processes in order to allow users a better understanding of the nature of the business, their role in it, and why the job that they do benefits the work of the company We assert that this kind of thinking is the essence of concurrent engineering implementation, and further that the systemigram process models uniquely stim ulate and organise such thinking.

Modelling frontal discontinuities in wind fields

A Bayesian procedure for the retrieval of wind vectors over the ocean using satellite borne scatterometers requires realistic prior near-surface wind field models over the oceans. We have implemented carefully chosen vector Gaussian Process models; however in some cases these models are too smooth to reproduce real atmospheric features, such as fronts. At the scale of the scatterometer observations, fronts appear as discontinuities in wind direction. Due to the nature of the retrieval problem a simple discontinuity model is not feasible, and hence we have developed a constrained discontinuity vector Gaussian Process model which ensures realistic fronts. We describe the generative model and show how to compute the data likelihood given the model. We show the results of inference using the model with Markov Chain Monte Carlo methods on both synthetic and real data.

Model evaluation and case series data

We discuss aggregation of data from neuropsychological patients and the process of evaluating models using data from a series of patients. We argue that aggregation can be misleading but not aggregating can also result in information loss. The basis for combining data needs to be theoretically defined, and the particular method of aggregation depends on the theoretical question and characteristics of the data. We present examples, often drawn from our own research, to illustrate these points. We also argue that statistical models and formal methods of model selection are a useful way to test theoretical accounts using data from several patients in multiple-case studies or case series. Statistical models can often measure fit in a way that explicitly captures what a theory allows; the parameter values that result from model fitting often measure theoretically important dimensions and can lead to more constrained theories or new predictions; and model selection allows the strength of evidence for models to be quantified without forcing this into the artificial binary choice that characterizes hypothesis testing methods. Methods that aggregate and then formally model patient data, however, are not automatically preferred to other methods. Which method is preferred depends on the question to be addressed, characteristics of the data, and practical issues like availability of suitable patients, but case series, multiple-case studies, single-case studies, statistical models, and process models should be complementary methods when guided by theory development.

Large volume metrology technologies for the light controlled factory

In the Light Controlled Factory part-to-part assembly and reduced weight will be enabled through the use of predictive fitting processes; low cost high accuracy reconfigurable tooling will be made possible by active compensation; improved control will allow accurate robotic machining; and quality will be improved through the use of traceable uncertainty based quality control throughout the production system. A number of challenges must be overcome before this vision will be realized; 1) controlling industrial robots for accurate machining; 2) compensation of measurements for thermal expansion; 3) Compensation of measurements for refractive index changes; 4) development of Embedded Metrology Tooling for in-tooling measurement and active tooling compensation; and 5) development of Software for the Planning and Control of Integrated Metrology Networks based on Quality Control with Uncertainty Evaluation and control systems for predictive processes. This paper describes how these challenges are being addressed, in particular the central challenge of developing large volume measurement process models within an integrated dimensional variation management (IDVM) system.

Flexible Gaussian process wind field models

This technical report builds on previous reports to derive the likelihood and its derivatives for a Gaussian Process with a modified Bessel function based covariance function. The full derivation is shown. The likelihood (with gradient information) can be used in maximum likelihood procedures (i.e. gradient based optimisation) and in Hybrid Monte Carlo sampling (i.e. within a Bayesian framework).

Non-zero mean Gaussian process prior wind field models

This report outlines the derivation and application of a non-zero mean, polynomial-exponential covariance function based Gaussian process which forms the prior wind field model used in 'autonomous' disambiguation. It is principally used since the non-zero mean permits the computation of realistic local wind vector prior probabilities which are required when applying the scaled-likelihood trick, as the marginals of the full wind field prior. As the full prior is multi-variate normal, these marginals are very simple to compute.

Life with sheepdogs:alternative metaphorical models of the doctoral research process revisited

The doctoral research process is the entry path for the academic profession. Traditionally it is explained by reference to another professional entry path, the industrial apprenticeship. Revisiting a paper and discussion originally held at the Marketing Education Group conference in 1991, we explore the implications and limitations of this metaphorical model, suggest alternatives and consider the interaction between student characteristics and supervisory approach. Through this process we offer marketing academics a vast range of unflattering metaphors to employ in describing themselves, their students, their supervisors and their colleagues.