Regression with input-dependent noise: A Gaussian process treatment

Gaussian processes provide natural non-parametric prior distributions over regression functions. In this paper we consider regression problems where there is noise on the output, and the variance of the noise depends on the inputs. If we assume that the noise is a smooth function of the inputs, then it is natural to model the noise variance using a second Gaussian process, in addition to the Gaussian process governing the noise-free output value. We show that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods. Our results on a synthetic data set give a posterior noise variance that well-approximates the true variance.

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.

Block GTM: Incorporating prior knowledge of covariance structure in data visualisation

Visualising data for exploratory analysis is a big challenge in scientific and engineering domains where there is a need to gain insight into the structure and distribution of the data. Typically, visualisation methods like principal component analysis and multi-dimensional scaling are used, but it is difficult to incorporate prior knowledge about structure of the data into the analysis. In this technical report we discuss a complementary approach based on an extension of a well known non-linear probabilistic model, the Generative Topographic Mapping. We show that by including prior information of the covariance structure into the model, we are able to improve both the data visualisation and the model fit.

Data visualisation and exploration with prior knowledge

Visualising data for exploratory analysis is a major challenge in many applications. Visualisation allows scientists to gain insight into the structure and distribution of the data, for example finding common patterns and relationships between samples as well as variables. Typically, visualisation methods like principal component analysis and multi-dimensional scaling are employed. These methods are favoured because of their simplicity, but they cannot cope with missing data and it is difficult to incorporate prior knowledge about properties of the variable space into the analysis; this is particularly important in the high-dimensional, sparse datasets typical in geochemistry. In this paper we show how to utilise a block-structured correlation matrix using a modification of a well known non-linear probabilistic visualisation model, the Generative Topographic Mapping (GTM), which can cope with missing data. The block structure supports direct modelling of strongly correlated variables. We show that including prior structural information it is possible to improve both the data visualisation and the model fit. These benefits are demonstrated on artificial data as well as a real geochemical dataset used for oil exploration, where the proposed modifications improved the missing data imputation results by 3 to 13%.

The colonisation of non-sterile wheat straw by fungi

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

The influence of non-metallic inclusions upon the properties of linepipe steels

The principal aim of this work was to determine the role of non-metallic inclusions in the process of hydrogen stepwise cracking (SWC). Additionally, the influence of inclusions upon the notch ductility of hydrogen charged (HC) and uncharged (UN) tensile specimens was examined. To obtain a basis for experiment a series of low carbon-manganese steels were prepared by induction melting. In order to produce variations in the composition, morphology, volume fraction, size and distribution of the inclusions the steel chemistry was adjusted prior to casting by additions of deoxidiser and Ca-Si injection. Sections of each ingot were hot rolled. Metallography, image analysis, mechanical tests and hydrogen SWC tests were then carried out. The volume fraction, morphology, and shape of inclusions influenced the tensile ductility of the steels. Marked anisotropy was found in the steels containing type II MnS inclusions at all rolling temperatures, whereas the fully Ca treated steel was isotropic. It was found that several inclusion parameters (projected length PL, mean free distance MFD, nearest-neighbour distance NND) correlated with fracture strain. An increase in inclusion volume fraction and/or the dimension of inclusions on a plane parallel to the plane of fracture led to a decrease in fracture strain. The inclusion parameters did not correlate with the fracture strains for the HC tensile specimens. However, large or clusters of inclusions acted as the principal sites for crack initiation. `Fisheyes' or areas of `flat' fracture were often found on these fracture surfaces. The criteria for SWC initiation was found to be either large inclusions or clusters of inclusions. As the PL of inclusions increased the probability of large SWCs occurring increased. SWC initiation at inclusions was believed to occur at a critical concentration of hydrogen. Factors which assisted the concentration of hydrogen at inclusions were discussed. None of the proposed mechanisms of hydrogen embrittlement could be identified as the single cause of SWC.

Exploratory data analysis with non-linear and missing data in geochemistry

Exploratory analysis of data seeks to find common patterns to gain insights into the structure and distribution of the data. In geochemistry it is a valuable means to gain insights into the complicated processes making up a petroleum system. Typically linear visualisation methods like principal components analysis, linked plots, or brushing are used. These methods can not directly be employed when dealing with missing data and they struggle to capture global non-linear structures in the data, however they can do so locally. This thesis discusses a complementary approach based on a non-linear probabilistic model. The generative topographic mapping (GTM) enables the visualisation of the effects of very many variables on a single plot, which is able to incorporate more structure than a two dimensional principal components plot. The model can deal with uncertainty, missing data and allows for the exploration of the non-linear structure in the data. In this thesis a novel approach to initialise the GTM with arbitrary projections is developed. This makes it possible to combine GTM with algorithms like Isomap and fit complex non-linear structure like the Swiss-roll. Another novel extension is the incorporation of prior knowledge about the structure of the covariance matrix. This extension greatly enhances the modelling capabilities of the algorithm resulting in better fit to the data and better imputation capabilities for missing data. Additionally an extensive benchmark study of the missing data imputation capabilities of GTM is performed. Further a novel approach, based on missing data, will be introduced to benchmark the fit of probabilistic visualisation algorithms on unlabelled data. Finally the work is complemented by evaluating the algorithms on real-life datasets from geochemical projects.

Study of synchronisation in chains of coupled non-linear oscillators and resonators

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Some aspects of the solution of non-linear differential equations

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Experiments on non-orthogonal signal representation

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

A description of the french passive for non-native speakers

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

The development of silicone sponge by using a non-toxic blowing agent

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

A comparisation of methods for the optimisation of a non-linear function subject to non-linear constraints

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

A non-linear encoder using a binary counterfor pulse-code modulation

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Interactive data in financial reporting:the construction of the non-professional investor

The Securities and Exchange Commission (SEC) in the United States and in particular its immediately past chairman, Christopher Cox, has been actively promoting an upgrade of the EDGAR system of disseminating filings. The new generation of information provision has been dubbed by Chairman Cox, "Interactive Data" (SEC, 2006). In October this year the Office of Interactive Disclosure was created(http://www.sec.gov/news/press/2007/2007-213.htm). The focus of this paper is to examine the way in which the non-professional investor has been constructed by various actors. We examine the manner in which Interactive Data has been sold as the panacea for financial market 'irregularities' by the SEC and others. The academic literature shows almost no evidence of researching non-professional investors in any real sense (Young, 2006). Both this literature and the behaviour of representatives of institutions such as the SEC and FSA appears to find it convenient to construct this class of investor in a particular form and to speak for them. We theorise the activities of the SEC and its chairman in particular over a period of about three years, both following and prior to the 'credit crunch'. Our approach is to examine a selection of the policy documents released by the SEC and other interested parties and the statements made by some of the policy makers and regulators central to the programme to advance the socio-technical project that is constituted by Interactive Data. We adopt insights from ANT and more particularly the sociology of translation (Callon, 1986; Latour, 1987, 2005; Law, 1996, 2002; Law & Singleton, 2005) to show how individuals and regulators have acted as spokespersons for this malleable class of investor. We theorise the processes of accountability to investors and others and in so doing reveal the regulatory bodies taking the regulated for granted. The possible implications of technological developments in digital reporting have been identified also by the CEO's of the six biggest audit firms in a discussion document on the role of accounting information and audit in the future of global capital markets (DiPiazza et al., 2006). The potential for digital reporting enabled through XBRL to "revolutionize the entire company reporting model" (p.16) is discussed and they conclude that the new model "should be driven by the wants of investors and other users of company information,..." (p.17; emphasis in the original). Here rather than examine the somewhat illusive and vexing question of whether adding interactive functionality to 'traditional' reports can achieve the benefits claimed for nonprofessional investors we wish to consider the rhetorical and discursive moves in which the SEC and others have engaged to present such developments as providing clearer reporting and accountability standards and serving the interests of this constructed and largely unknown group - the non-professional investor.