Mathematical Sciences Research Collection

Anisotropic spatial clustering of TB in cattle - the implications for control policy

Sat, 01 Jan 2011 00:00:00 GMT

Anisotropic spatial clustering of TB in cattle - the implications for control policy Kelly, Gabrielle E. Bovine TB is a disease that affects cattle and the wildlife badger, species Meles meles, in Ireland and the UK, and badgers have been implicated in the spread of the disease in cattle. Efforts to eradicate the disease that have included localized badger culling, have not been successful. In a study to understand how the disease spreads, Kelly and More [1] determined that the disease spatially clusters in cattle herds and estimated the practical spatial ranges at which this occurs. We extend this work by examining possible anisotropy in clustering and the consequences for TB control policy. 1st Conference on Spatial Statistics 2011 – Mapping Global Change, Enschede, The Netherlands, March, 2011

Clustering Ordinal Data via Latent Variable Models

Mon, 01 Apr 2013 00:00:00 GMT

Clustering Ordinal Data via Latent Variable Models McParland, Damien; Gormley, Claire Item response modelling is a well established method for analysing ordinal response data. Ordinal data are typically collected as responses to a number of questions or items. The observed data can be viewed as discrete versions of an underlying latent Gaussian variable. Item response models assume that this latent variable (and therefore the observed ordinal response) is a function of both respondent specific and item specific parameters. However, item response models assume a homogeneous population in that the item specific parameters are assumed to be the same for all respondents. Often a population is heterogeneous and clusters of respondents exist; members of different clusters may view the items differently. A mixture of item response models is developed to provide clustering capabilities in the context of ordinal response data. The model is estimated within the Bayesian paradigm and is illustrated through an application to an ordinal response data set resulting from a clinical trial involving self-assessment of arthritis. IFCS 2013 Conference of the International Federation of Classification Societies, Tilburg University, The Netherlands, from July 14-17, 2013

A long term observational study of the impact of badger removal on herd restrictions due to bovine TB in the Irish midlands during 1989-2004

Wed, 01 Oct 2008 00:00:00 GMT

A long term observational study of the impact of badger removal on herd restrictions due to bovine TB in the Irish midlands during 1989-2004 Kelly, Gabrielle E.; Condon, J.; More, Simon John; Dolan, L.; Higgins, I.; Eves, J. An observational study was carried out, using data collected from four areas in the Irish midlands, between 1989 and 2004, to critically evaluate the long-term effects of proactive badger culling and to provide insights into reactive badger culling tuberculosis (TB) prevalence in cattle. Confirmed cattle herd TB incidence is the outcome measure used throughout. Relative to reactive culling, proactive badger culling was associated with a decrease in incidence in each of the 16 years of observation, which encompassed periods of both intensive and less-intensive badger removal. By 2004, we observed a decrease of 22% [95% confidence interval (CI) 15-29, P<0.001] in the entire proactive and 37% (95% CI 25–47, P<0.001), in the inner proactive removal areas. The size of the decrease increased with time (P=0.055). There was a decrease (constant over time) of at least 14% (95% CI 76–97, P=0.013) in incidence in the inner compared to the outer control area (herds ≤2 km, >2 km, from proactive removal area boundaries, respectively). Incidence in the outer proactive removal area (herds <1.6 km from the proactive removal boundary) was similar to the inner control area (P=0.890). Incidence in the outer control area and total control area, compared to a neighbouring area some distance away, increased over the course of the study. Differences with the total control area were not statistically significant but the outer control area was 11% higher than the neighbouring area by 2004 (borderline significance P=0.057).

Body mass index and height over three generations: evidence from the Lifeways cross-generational cohort study

Sun, 01 Jan 2012 00:00:00 GMT

Body mass index and height over three generations: evidence from the Lifeways cross-generational cohort study Murrin, Celine; Kelly, Gabrielle E.; Tremblay, Richard E.; Kelleher, Cecily Background: Obesity and its measure of body mass index are strongly determined by parental body size. Debate continues as to whether both parents contribute equally to offspring body mass which is key to understanding the aetiology of the disease. The aim of this study was to use cohort data from three generations of one family to examine the relative maternal and paternal associations with offspring body mass index and how these associations compare with family height to demonstrate evidence of genetic or environmental cross-generational transmission. Methods: 669 of 1082 families were followed up in 2007/8 as part of the Lifeways study, a prospective observational cross-generation linkage cohort. Height and weight were measured in 529 Irish children aged 5 to 7 years and were self-reported by parents and grandparents. All adults provided information on self-rated health, education status, and indicators of income, diet and physical activity. Associations between the weight, height, and body mass index of family members were examined with mixed models and heritability estimates computed using linear regression analysis. Results: Self-rated health was associated with lower BMI for all family members, as was age for children. When these effects were accounted for evidence of familial associations of BMI from one generation to the next was more apparent in the maternal line. Heritability estimates were higher (h2 = 0.40) for mother-offspring pairs compared to father-offspring pairs (h2 = 0.22). In the previous generation, estimates were higher between mothersparents (h2 = 0.54-0.60) but not between fathers-parents (h2 = -0.04-0.17). Correlations between mother and offspring across two generations remained significant when modelled with fixed variables of socioeconomic status, health, and lifestyle. A similar analysis of height showed strong familial associations from maternal and paternal lines across each generation. Conclusions: This is the first family cohort study to report an enduring association between mother and offspring BMI over three generations. The evidence of BMI transmission over three generations through the maternal line in an observational study corroborates the findings of animal studies. A more detailed analysis of geno and phenotypic data over three generations is warranted to understand the nature of this maternal-offspring relationship.

Spatial clustering of TB-infected cattle herds prior to and following proactive badger removal

Mon, 01 Aug 2011 00:00:00 GMT

Spatial clustering of TB-infected cattle herds prior to and following proactive badger removal Kelly, Gabrielle E.; More, Simon John Bovine tuberculosis (TB) is primarily a disease of cattle. In both Ireland and the UK, badgers (Meles meles) are an important wildlife reservoir of infection. This paper examined the hypothesis that TB is spatially correlated in cattle herds, established the range of correlation and the effect, if any, of proactive badger removal on this. We also re-analysed data from the Four Area Project in Ireland, a large-scale intervention study aimed at assessing the effect of proactive badger culling on bovine TB incidence in cattle herds, taking possible spatial correlation into account. We established that infected herds are spatially correlated (the scale of spatial correlation is presented), but at a scale that varies with time and in different areas. Spatial correlation persists following proactive badger removal.

Estimating the extent of spatial association of Mycobacterium bovis infection in badgers in Ireland

Mon, 01 Feb 2010 00:00:00 GMT

Estimating the extent of spatial association of Mycobacterium bovis infection in badgers in Ireland Kelly, Gabrielle E.; McGrath, Guy; More, Simon John Mycobacterium bovis infects the wildlife species badgers Meles meles who are linked with the spread of the associated disease tuberculosis (TB) in cattle. Control of livestock infections depends in part on the spatial and social structure of the wildlife host. Here we describe spatial association of M. bovis infection in a badger population using data from the first year of the Four Area Project in Ireland. Using second-order intensity functions, we show there is strong evidence of clustering of TB cases in each the four areas, i.e. a global tendency for infected cases to occur near other infected cases. Using estimated intensity functions, we identify locations where particular strains of TB cluster. Generalized linear geostatistical models are used to assess the practical range at which spatial correlation occurs and is found to exceed 6 in all areas. The study is of relevance concerning the scale of localized badger culling in the control of the disease in cattle.

Spatio-Temporal Modelling of TB in Cattle Herds

Wed, 01 Aug 2012 00:00:00 GMT

Spatio-Temporal Modelling of TB in Cattle Herds Kelly, Gabrielle E. We examine spatial association of bovine TB in cattle herds using data from Ireland. Badgers (Meles meles), a protected species under the Wildlife Act 1976 (OAG 2012), have been implicated in the spread of the disease in cattle. Current disease control policies include reactive culling (in response to TB outbreaks) of badgers in the index and neighbouring farms. Kelly and More (2011) using generalized linear geostatistical models, established that TB clusters in cattle herds and estimated the practical spatial ranges at which this occurs. Here this work is extended by taking into account possible anisotropy. Changes in spatial association over two time periods are also examined. The results have direct implications for establishing scale and direction in reactive culling. They are also of import regarding the evaluation of vaccines for badgers and cattle.

Boundary behaviour of functions which possess universal Taylor series

Fri, 01 Feb 2013 00:00:00 GMT

Boundary behaviour of functions which possess universal Taylor series Gardiner, Stephen J. It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess ‘universal’ Taylor series expansions about ζ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in ℂ\ Ω that have connected complement. This paper establishes a strong unboundedness property for such functions near every boundary point. The result is new even in the case of the disc, where it strengthens work of several authors.

Determination of a universal series

Sun, 01 Jan 2012 00:00:00 GMT

Determination of a universal series Mouze, Augustin; Nestoridis, Vassili; Papadoperakis, Ioannis; Tsirivas, Nikolaos The known proofs for universal Taylor series do not determine a specific universal Taylor series. In the present paper, we isolate a specific universal Taylor series by modifying the proof in [30]. Thus we determine all Taylor coefficients of a specific universal Taylor series on the disc or on a polygonal domain. Furthermore in non simply connected domains, when universal Taylor series exist, we can construct a sequence of specific rational functions converging to a universal function, provided the boundary is good enough. The solution uses an infinite denumerable procedure and a finite number of steps is not sufficient. However we solve a Runge's type problem in a finite number of steps.

Ostrowski-type theorems for harmonic functions

Sun, 15 Jul 2012 00:00:00 GMT

Ostrowski-type theorems for harmonic functions Manolaki, Myrto Ostrowski showed that there are intimate connections between the gap structure of a Taylor series and the behaviour of its partial sums outside the disk of convergence. This paper investigates the corresponding problem for the homogeneous polynomial expansion of a harmonic function. The results for harmonic functions display new features in the case of higher dimensions.

Two-phase quadrature domains

Sun, 01 Jan 2012 00:00:00 GMT

Two-phase quadrature domains Gardiner, Stephen J.; Sjödin, Tomas Recent work on two-phase free boundary problems has led to the investigation of a new type of quadrature domain for harmonic functions. This paper develops a method of constructing such quadrature domains based on the technique of partial balayage, which has proved to be a useful tool in the study of one-phase quadrature domains and Hele-Shaw flows.

Sentiment Analysis of Online Media

Tue, 18 Dec 2012 00:00:00 GMT

Sentiment Analysis of Online Media Salter-Townshend, Michael; Murphy, Thomas Brendan A joint model for annotation bias and document classification is presented in the context of media sentiment analysis. We consider an Irish online media data set comprising online news articles with user annotations of negative, positive or irrelevant impact on the Irish economy. The joint model combines a statistical model for user annotation bias and a Naive Bayes model for the document terms. An EM algorithm is used to estimate the annotation bias model, the unobserved biases in the user annotations, the classifier parameters and the sentiment of the articles. The joint modeling of both the user biases and the classifier is demonstrated to be superior to estimation of the bias followed by the estimation of the classifier parameters. GfKl 2011: Joint Conference of the German Classification Society (GfKl) and the German Association for Pattern Recognition (DAGM) August 31 to September 2, 2011 and the IFCS 2011: Symposium of the International Federation of Classification Societies (IFCS) August 30, 2011, Frankfurt am Main, Germany

Recent progress on fine differentiability and fine harmonicity

Sat, 15 Dec 2012 00:00:00 GMT

Recent progress on fine differentiability and fine harmonicity Gardiner, Stephen J. This paper describes recent results concerning the notions of differentiability and harmonicity with respect to the ne topology of classical potential theory. Complex Analysis and Potential Theory : a conference in honour of Paul M. Gauthier and Kohur Gowrisankaran, Montreal, June 20-23, 2011

A generalization of universal Taylor series in simply connected domains

Sun, 01 Apr 2012 00:00:00 GMT

A generalization of universal Taylor series in simply connected domains Tsirivas, Nikolaos Let Ω be a simply connected proper subdomain of the complex plane and z0 be a point in Ω. It is known that there are holomorphic functions f on Ω for which the partial sums (Sn(f,z0)) of the Taylor series about z0 have universal approximation properties outside Ω. In this paper we investigate what can be said for the sequence (βnSn(f,z0)) when (βn) is a sequence of complex numbers. We also study a related analogue of a classical theorem of Seleznev concerning the case where the radius of convergence of the universal power series is zero.

Existence of universal Taylor series for non-simply connected domains

Sun, 27 May 2012 00:00:00 GMT

Existence of universal Taylor series for non-simply connected domains Gardiner, Stephen J. It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess “universal” Taylor series expansions about ζ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in ℂ\Ω that have connected complement. This paper shows, for nonsimply connected domains Ω, how issues of capacity, thinness and topology affect the existence of holomorphic functions on Ω that have universal Taylor series expansions about a given point.

Positivity properties for the clamped plate boundary problem on the ellipse and strip

Fri, 01 Jun 2012 00:00:00 GMT

Positivity properties for the clamped plate boundary problem on the ellipse and strip Render, Hermann; Ghergu, Marius The positivity preserving property for the biharmonic operator with Dirichlet boundary condition is investigated. We discuss here the case where the domain is an ellipse (that may degenerate to a strip) and the data is a polynomial function. We provide various conditions for which the positivity is preserved.

Spatio-temporal modeling of TB in cattle herds

Wed, 01 Aug 2012 00:00:00 GMT

Spatio-temporal modeling of TB in cattle herds Kelly, Gabrielle E. We examine spatial association of bovine TB in cattle herds using data from Ireland. Badgers (Meles meles), a protected species under the Wildlife Act 1976 (OAG 2012), have been implicated in the spread of the disease in cattle. Current disease control policies include reactive culling (in response to TB outbreaks) of badgers in the index and neighbouring farms. Kelly and More (2011) using generalized linear geostatistical models, established that TB clusters in cattle herds and estimated the practical spatial ranges at which this occurs. Here this work is extended by taking into account possible anisotropy. Changes in spatial association over two time periods are also examined. The results have direct implications for establishing scale and direction in reactive culling. They are also of import regarding the evaluation of vaccines for badgers and cattle.

Isotropy over function fields of Pfister forms

Sun, 01 Jul 2012 00:00:00 GMT

Isotropy over function fields of Pfister forms O'Shea, James The question of which quadratic forms become isotropic when extended to the function field of a given form is studied. A formula for the minimum dimension of the minimal isotropic forms associated to such extensions is given, and some consequences thereof are outlined. Especial attention is devoted to function fields of Pfister forms. Here, the relationship between excellence concepts and the isotropy question is explored. Moreover, in the case where the ground field is formally real and has finite Hasse number, the isotropy question is answered for forms of sufficiently large dimension.

Sentiment analysis of online media

Sun, 01 Jan 2012 00:00:00 GMT

Sentiment analysis of online media Salter-Townshend, Michael; Murphy, Thomas Brendan A joint model for annotation bias and document classification is presented in the context of media sentiment analysis. We consider an Irish online media data set comprising online news articles with user annotations of negative, positive or irrelevant impact on the Irish economy. The joint model combines a statistical model for user annotation bias and a Naive Bayes model for the document terms. An EM algorithm is used to estimate the annotation bias model, the unobserved biases in the user annotations, the classifier parameters and the sentiment of the articles. The joint modeling of both the user biases and the classifier is demonstrated to be superior to estimation of the bias followed by the estimation of the classifier parameters. Paper presented at the DAGM-GfKl/IFCS 2011, Joint Conference of the German Classification Society (GfKl) and the German Association for Pattern Recognition (DAGM), August 31 to September 2, 2011 and at the IFCS 2011 Symposium of the International Federation of Classification Societies (IFCS), August 30, 2011, Frankfurt am Main, Germany

Semi-supervised linear discriminant analysis

Thu, 01 Dec 2011 00:00:00 GMT

Semi-supervised linear discriminant analysis Toher, Deirdre; Downey, Gerard; Murphy, Thomas Brendan Fisher's linear discriminant analysis is one of the most commonly used and studied classification methods in chemometrics. The method finds a projection of multivariate data into a lower dimensional space so that the groups in the data are well separated. The resulting projected values are subsequently used to classify unlabeled observations into the groups. A semi-supervised version of Fisher's linear discriminant analysis is developed, so that the unlabeled observations are also used in the model fitting procedure. This approach is advantageous when few labeled and many unlabeled observations are available. The semi-supervised linear discriminant analysis method is demonstrated on a number of data sets where it is shown to yield better separation of the groups and improved classification over Fisher's linear discriminant analysis.

Reducing errors of wind speed forecasts by an optimal combination of post-processing methods

Tue, 13 Sep 2011 00:00:00 GMT

Reducing errors of wind speed forecasts by an optimal combination of post-processing methods Sweeney, Conor; Lynch, Peter; Nolan, Paul Seven adaptive approaches to post-processing wind speed forecasts are discussed and compared. 48-hour forecasts are run at horizontal resolutions of 7 km and 3 km for a domain centred over Ireland. Forecast wind speeds over a two year period are compared to observed wind speeds at seven synoptic stations around Ireland and skill scores calculated. Two automatic methods for combining forecast streams are applied. The forecasts produced by the combined methods give bias and root mean squared errors that are better than the numerical weather prediction forecasts at all station locations. One of the combined forecast methods results in skill scores that are equal to or better than all of its component forecast streams. This method is straightforward to apply and should prove beneficial in operational wind forecasting.

The two-child paradox : dichotomy and ambiguity

Fri, 01 Jul 2011 00:00:00 GMT

The two-child paradox : dichotomy and ambiguity Lynch, Peter Given that one of the children in a two-child family is a boy, what are the chances that the other is also a boy. The intuitive answer is 50 : 50. More careful investigation leads us to a 1-in-3 chance. We investigate circumstances under which these answers are correct. The imposition of further conditions yields some very surprising results.

Initialization

Sun, 01 Aug 2010 00:00:00 GMT

Initialization Lynch, Peter; Huang, Xiang-Yu The spectrum of atmospheric motions is vast, encompassing phenomena having periods ranging from seconds to millennia. The motions of interest to the forecaster typically have time-scales of a day or longer, but the mathematical models used for numerical prediction describe a broader span of dynamical features than those of direct concern. For many purposes these higher frequency components can be regarded as noise contaminating the motions of meteorological interest. The elimination of this noise is achieved by adjustment of the initial fields, a process called initialization.

Weather and climate forecasting : chronicle of a revolution

Tue, 01 Jun 2010 00:00:00 GMT

Weather and climate forecasting : chronicle of a revolution Lynch, Peter Remarkable advances in weather forecasts during the past half-century have brought great benefits to humanity. Accurate forecasts save many lives, and early warnings mitigate the worst effects of extreme weather events, when they are available. Detailed, accurate forecasts are of huge economic value, with numerous studies showing that the benefits of forecasts outweigh the costs many times over. Advances in climate modeling over the past fifty years have also been outstanding. General circulation models have been developed and applied to examine the factors causing changes in our climate, and their likely timing and severity.

On resonant Rossby-Haurwitz triads

Fri, 01 May 2009 00:00:00 GMT

On resonant Rossby-Haurwitz triads Lynch, Peter The dynamics of non-divergent flow on a rotating sphere are described by the conservation of absolute vorticity. The analytical study of the non-linear barotropic vorticity equation is greatly facilitated by the expansion of the solution in spherical harmonics and truncation at low order. The normal modes are the well-known Rossby–Haurwitz (RH) waves, which represent the natural oscillations of the system. Triads of RH waves, which satisfy conditions for resonance, are of critical importance for the distribution of energy in the atmosphere. We show how non-linear interactions of resonant RH triads may result in dynamic instability of large-scale components. We also demonstrate a mathematical equivalence between the equations for an orographically forced triad and a simple mechanical system, the forced-damped swinging spring. This equivalence yields insight concerning the bounded response to a constant forcing in the absence of damping. An examination of triad interactions in atmospheric reanalysis data would be of great interest.

A latent space mapping for link prediction

Sat, 11 Dec 2010 00:00:00 GMT

A latent space mapping for link prediction Brew, Anthony; Salter-Townshend, Michael Network modeling can be approached using either discriminative or probabilistic models. In the task of link prediction a probabilistic model will give a probability for the existence of a link; while in some scenarios this may be beneficial, in others a hard discriminative boundary needs to be set. Hence the use of a discriminative classifier is preferable. In domains such as image analysis and speaker recognition, probabilistic models have been used as a mechanism from which features can be extracted. This paper examines using a probabilistic model built on the entire graph to extract features to predict the existence of unknown links between two nodes. It demonstrates how features extracted from the model as well as the predicted probability of a link existing can aid the classification process. NIPS Workshop on Networks across Disciplines in Theory and Applications, 11th December 2010, Whistler BC, Canada

Precession and recession of the rock'n'roller

Wed, 30 Sep 2009 00:00:00 GMT

Precession and recession of the rock'n'roller Lynch, Peter; Bustamante, Miguel We study the dynamics of a spherical rigid body that rocks and rolls on a plane under the effect of gravity. The distribution of mass is non-uniform and the centre of mass does not coincide with the geometric centre. The symmetric case, with moments of inertia I1 = I2 < I3, is integrable and themotion is completely regular. Three known conservation laws are the total energy E, Jellett’s quantity QJ and Routh’s quantity QR. When the inertial symmetry I1 = I2 is broken, even slightly, the character of the solutions is profoundly changed and new types of motion become possible. We derive the equations governing the general motion and present analytical and numerical evidence of the recession, or reversal of precession, that has been observed in physical experiments. We present an analysis of recession in terms of critical lines dividing the (QR,QJ ) plane into four dynamically disjoint zones. We prove that recession implies the lack of conservation of Jellett’s and Routh’s quantities, by identifying individual reversals as crossings of the orbit (QR(t ),QJ (t)) through the critical lines. Consequently, a method is found to produce a large number of initial conditions so that the system will exhibit recession.

Adaptive post-processing of short-term wind forecasts for energy applications

Fri, 01 Apr 2011 00:00:00 GMT

Adaptive post-processing of short-term wind forecasts for energy applications Sweeney, Conor; Lynch, Peter We present a new method of reducing the error in predicted wind speed, thus enabling better management of wind energy facilities. A numerical weather prediction model, COSMO, was used to produce 48 h forecast data every day in 2008 at horizontal resolutions of 10 and 3 km. A new adaptive statistical method was applied to the model output to improve the forecast skill. The method applied corrective weights to a set of forecasts generated using several post-processing methods. The weights were calculated based on the recent skill of the different forecasts. The resulting forecast data were compared with observed data, and skill scores were calculated to allow comparison between different post-processing methods. The total root mean square error performance of the composite forecast is superior to that of any of the individual methods.

From Richardson to early numerical weather prediction

Wed, 01 Dec 2010 00:00:00 GMT

From Richardson to early numerical weather prediction Lynch, Peter The development of computer models for numerical simulation of the atmosphere and oceans is one of the great scientific triumphs of the past fifty years. These models have added enormously to our understanding of the complex processes in the atmosphere and oceans. The consequences for humankind of ongoing climate change will be far-reaching. Earth system models are the best means we have of predicting the future of our climate. The basic ideas of numerical forecasting and climate modeling were developed about a century ago, long before the first electronic computer was constructed. However, advances on several fronts were necessary before numerical prediction could be put into practice. A fuller understanding of atmospheric dynamics allowed the development of simplified systems of equations; regular observations of the free atmosphere provided the initial conditions; stable finite difference schemes were developed; and powerful electronic computers provided a practical means of carrying out the calculations required to predict the changes in the weather. In this chapter, we trace the history of computer forecasting from Richardson’s prodigious manual computation, through the ENIAC (Electronic Numerical Integrator and Computer) integrations to the early days of operational numerical weather prediction and climate modeling. The useful range of deterministic prediction is increasing by about one day each decade. We set the scene for the story of the remarkable progress in weather forecasting and in climate modeling over the past fifty years, which will be treated in subsequent chapters.

Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications

Mon, 01 Mar 2010 00:00:00 GMT

Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications Murphy, Thomas Brendan; Dean, Nema; Raftery, Adrian E. Food authenticity studies are concerned with determining if food samples have been correctly labelled or not. Discriminant analysis methods are an integral part of the methodology for food authentication. Motivated by food authenticity applications, a model-based discriminant analysis method that includes variable selection is presented. The discriminant analysis model is fitted in a semi-supervised manner using both labeled and unlabeled data. The method is shown to give excellent classification performance on several high-dimensional multiclass food authenticity datasets with more variables than observations. The variables selected by the proposed method provide information about which variables are meaningful for classification purposes. A headlong search strategy for variable selection is shown to be efficient in terms of computation and achieves excellent classification performance. In applications to several food authenticity datasets, our proposed method outperformed default implementations of Random Forests, AdaBoost, transductive SVMs and Bayesian Multinomial Regression by substantial margins.

Laplace transform integration of the shallow-water equations. Part 2: Lagrangian formulation and orographic resonance

Fri, 01 Apr 2011 00:00:00 GMT

Laplace transform integration of the shallow-water equations. Part 2: Lagrangian formulation and orographic resonance Clancy, Colm; Lynch, Peter In this paper we combine the Laplace transform (LT) scheme with a semi- Lagrangian advection scheme, and implement it in a shallow water model. It is compared to a reference model using the semi-implicit (SI) scheme, with both Eulerian and Lagrangian advection. We show that the LT scheme is accurate and computationally competitive with these reference schemes. We also show, both analytically and numerically, that the LT scheme is free from the problem of orographic resonance that is found with semi-implicit schemes.

Laplace transform integration of the shallow-water equations. Part 1: Eulerian formulation and Kelvin waves

Fri, 01 Apr 2011 00:00:00 GMT

Laplace transform integration of the shallow-water equations. Part 1: Eulerian formulation and Kelvin waves Clancy, Colm; Lynch, Peter A filtering integration scheme is developed, using a modification of the contour used to invert the Laplace transform (LT). It is shown to eliminate components with frequencies higher than a specified cut-off value. Thus it is valuable for integrations of the equations governing atmospheric flow. The scheme is implemented in a shallow water model with an Eulerian treatment of advection. It is compared to a reference model using the semi-implicit (SI) scheme. The LT scheme is shown to treat dynamically important Kelvin waves more accurately than the SI scheme.

Sums of squares in certain quaternion and octonion algebras

Tue, 01 Mar 2011 00:00:00 GMT

Sums of squares in certain quaternion and octonion algebras O'Shea, James Formulae for the levels and sublevels of certain quaternion and octonion algebras are established. Corollaries concerning the equality of levels and sublevels of quaternion algebras with those of associated octonion algebras are presented.

Model-Based clustering of microarray expression data via latent Gaussian mixture models

Mon, 01 Nov 2010 00:00:00 GMT

Model-Based clustering of microarray expression data via latent Gaussian mixture models McNicholas, Paul D.; Murphy, Thomas Brendan In recent years, work has been carried out on clustering gene expression microarray data. Some approaches are developed from an algorithmic viewpoint whereas others are developed via the application of mixture models. In this article, a family of eight mixture models which utilizes the factor analysis covariance structure is extended to 12 models and applied to gene expression microarray data. This modelling approach builds on previous work by introducing a modified factor analysis covariance structure, leading to a family of 12 mixture models, including parsimonious models. This family of models allows for the modelling of the correlation between gene expression levels even when the number of samples is small. Parameter estimation is carried out using a variant of the expectation–maximization algorithm and model selection is achieved using the Bayesian information criterion. This expanded family of Gaussian mixture models, known as the expanded parsimonious Gaussian mixture model (EPGMM) family, is then applied to two well-known gene expression data sets.

Probabilistic principal component analysis for metabolomic data

Tue, 23 Nov 2010 00:00:00 GMT

Probabilistic principal component analysis for metabolomic data Nyamundanda, Gift; Brennan, Lorraine; Gormley, Isobel Claire Background: Data from metabolomic studies are typically complex and high-dimensional. Principal component analysis (PCA) is currently the most widely used statistical technique for analyzing metabolomic data. However, PCA is limited by the fact that it is not based on a statistical model. Results: Here, probabilistic principal component analysis (PPCA) which addresses some of the limitations of PCA, is reviewed and extended. A novel extension of PPCA, called probabilistic principal component and covariates analysis (PPCCA), is introduced which provides a flexible approach to jointly model metabolomic data and additional covariate information. The use of a mixture of PPCA models for discovering the number of inherent groups in metabolomic data is demonstrated. The jackknife technique is employed to construct confidence intervals for estimated model parameters throughout. The optimal number of principal components is determined through the use of the Bayesian Information Criterion model selection tool, which is modified to address the high dimensionality of the data. Conclusions: The methods presented are illustrated through an application to metabolomic data sets. Jointly modeling metabolomic data and covariates was successfully achieved and has the potential to provide deeper insight to the underlying data structure. Examination of confidence intervals for the model parameters, such as loadings, allows for principled and clear interpretation of the underlying data structure. A software package called MetabolAnalyze, freely available through the R statistical software, has been developed to facilitate implementation of the presented methods in the metabolomics field.

Model-based clustering of longitudinal data

Mon, 01 Mar 2010 00:00:00 GMT

Model-based clustering of longitudinal data McNicholas, Paul D.; Murphy, Thomas Brendan A new family of mixture models for the model-based clustering of longitudinal data is introduced. The covariance structures of eight members of this new family of models are given and the associated maximum likelihood estimates for the parameters are derived via expectation-maximization (EM) algorithms. The Bayesian information criterion is used for model selection and a convergence criterion based on Aitken’s acceleration is used to determine convergence of these EM algorithms. This new family of models is applied to yeast sporulation time course data, where the models give good clustering performance. Further constraints are then imposed on the decomposition to allow a deeper investigation of correlation structure of the yeast data. These constraints greatly extend this new family of models, with the addition of many parsimonious models.

Clustering ranked preference data using sociodemographic covariates

Fri, 01 Jan 2010 00:00:00 GMT

Clustering ranked preference data using sociodemographic covariates Gormley, Isobel Claire; Murphy, Thomas Brendan Ranked preference data arise when a set of judges rank, in order of their preference, a set of objects. Such data arise in preferential voting systems and market research surveys. Covariate data associated with the judges are also often recorded. Such covariate data should be used in conjunction with preference data when drawing inferences about judges. To cluster a population of judges, the population is modelled as a collection of homogeneous groups. The Plackett-Luce model for ranked data is employed to model a judge’s ranked preferences within a group. A mixture of Plackett-Luce models is employed to model the population of judges, where each component in the mixture represents a group of judges. Mixture of experts models provide a framework in which covariates are included in mixture models. Covariates are included through the mixing proportions and the component density parameters. A mixture of experts model for ranked preference data is developed by combining a mixture of experts model and a mixture of Plackett-Luce models. Particular attention is given to the manner in which covariates enter the model. The mixing proportions and group specific parameters are potentially dependent on covariates. Model selection procedures are employed to choose optimal models. Model parameters are estimated via the ‘EMM algorithm’, a hybrid of the Expectation-Maximization and the Minorization-Maximization algorithms. Examples are provided through a menu survey and through Irish election data. Results indicate mixture modelling using covariates is insightful when examining a population of judges who express preferences.

Preferences in college applications - a nonparametric Bayesian analysis of top-10 rankings

Fri, 10 Dec 2010 00:00:00 GMT

Preferences in college applications - a nonparametric Bayesian analysis of top-10 rankings Ali, Alnur; Murphy, Thomas Brendan; Meila, Marina; Chen, Harr Applicants to degree courses in Irish colleges and universities rank up to ten degree courses from a list of over ﬁve hundred. These data provide a wealth of information concerning applicant degree choices. A Dirichlet process mixture of generalized Mallows models are used to explore data from a cohort of applicants. We ﬁnd strong and diverse clusters, which in turn gains us important insights into the workings of the system. No previously tried models or analysis technique are able to model the data with comparable accuracy. NIPS Workshop on Computational Social Science and the Wisdom of Crowds, December 10th 2010, Whistler, Canada

Mixture of experts modelling with social science applications

Fri, 01 Apr 2011 00:00:00 GMT

Mixture of experts modelling with social science applications Gormley, Isobel Claire; Murphy, Thomas Brendan

Variational Bayesian inference for the Latent Position Cluster Model

Tue, 01 Dec 2009 00:00:00 GMT

Variational Bayesian inference for the Latent Position Cluster Model Salter-Townshend, Michael; Murphy, Thomas Brendan Many recent approaches to modeling social networks have focussed on embedding the actors in a latent “social space”. Links are more likely for actors that are close in social space than for actors that are distant in social space. In particular, the Latent Position Cluster Model (LPCM) [1] allows for explicit modelling of the clustering that is exhibited in many network datasets. However, inference for the LPCM model via MCMC is cumbersome and scaling of this model to large or even medium size networks with many interacting nodes is a challenge. Variational Bayesian methods offer one solution to this problem. An approximate, closed form posterior is formed, with unknown variational parameters. These parameters are tuned to minimize the Kullback-Leibler divergence between the approximate variational posterior and the true posterior, which known only up to proportionality. The variational Bayesian approach is shown to give a computationally efficient way of fitting the LPCM. The approach is demonstrated on a number of data sets and it is shown to give a good fit. Analyzing Networks and Learning with Graphs Workshop at 23rd annual conference on Neural Information Processing Systems (NIPS 2009), Whister, December 11 2009

Sets of determination for the Nevanlinna class

Sat, 06 Nov 2010 00:00:00 GMT

Sets of determination for the Nevanlinna class Gardiner, Stephen J. This paper characterizes the subsets E of the unit disc D with the property that the supremum of |f| over E equals the supremum over D for all functions f in the Nevanlinna class.

Bounds on the levels of composition algebras

Fri, 01 Jan 2010 00:00:00 GMT

Bounds on the levels of composition algebras O'Shea, James Certain families of quaternion and octonion algebras are conjectured to be of level and sublevel n. A proof of this conjecture is offered in the case where n is a power of two. Hoffmann's proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted. Alternative constructions of quaternion and octonion algebras are introduced and justified in the case where n is a multiple of a two power.

Levels and sublevels of composition algebras over p-adic function fields

Tue, 01 Jan 2008 00:00:00 GMT

Levels and sublevels of composition algebras over p-adic function fields O'Shea, James; Geel, Jan Van In [O'S], the level and sublevel of composition algebras are studied, wherein these quantities are determined for those algebras defined over local fields. In this paper, the level and sublevel of composition algebras, of dimension 4 and 8 over rational function fields over local non-dyadic fields, are determined completely in terms of the local ramification data of the algebras. The proofs are based on the "classification" of quadratic forms over such fields, as is given in [PS].

Levels and sublevels of composition algebras

Mon, 01 Jan 2007 00:00:00 GMT

Levels and sublevels of composition algebras O'Shea, James Lewis' and Leep's bounds on the level and sublevel of quaternion algebras are extended to the class of composition algebras. Some simple constructions of composition algebras of known level values are given. In addition, octonion algebras of sublevel 3 are presented.

Universal Taylor series for non-simply connected domains

Sat, 01 May 2010 00:00:00 GMT

Universal Taylor series for non-simply connected domains Gardiner, Stephen J.; Tsirivas, Nikolaos It is known that, for any simply connected proper subdomain Omega of the complex plane and any point zeta in Omega, there are holomorphic functions on Omega that have "universal" Taylor series expansions about zeta; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in C\Omega that have connected complement. This note shows that this phenomenon can break down for non-simply connected domains Omega, even when C\Omega is compact. This answers a question of Melas and disproves a conjecture of Müller, Vlachou and Yavrian.

Classification using distance nearest neighbours

Fri, 01 Jan 2010 00:00:00 GMT

Classification using distance nearest neighbours Friel, Nial; Pettitt, Anthony This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label should depend more on class labels which are closer in the feature space, than those which are further away. Our approach builds on previous work by Holmes and Adams (2002, 2003) and Cucala et al. (2009). Our work shares many of the advantages of these approaches in providing a probabilistic basis for the statistical inference. In comparison to previous work, we present a more efficient computational algorithm to overcome the intractability of the Markov random field model. The results of our algorithm are encouraging in comparison to the k-nearest neighbour algorithm.

Deterministic Bayesian inference for the p* model

Fri, 01 Jan 2010 00:00:00 GMT

Deterministic Bayesian inference for the p* model Austad, Haakon; Friel, Nial The p* model is widely used in social network analysis. The likelihood of a network under this model is impossible to calculate for all but trivially small networks. Various approximation have been presented in the literature, and the pseudolikelihood approximation is the most popular. The aim of this paper is to introduce two likelihood approximations which have the pseudolikelihood estimator as a special case. We show, for the examples that we have considered, that both approximations result in improved estimation of model parameters with respect to the standard methodological approaches. We provide a deterministic approach and also illustrate how Bayesian model choice can be carried out in this setting. 13th International conference on Artificial Intelligence and Statistics (AISTATS, 2010), Chia Laguna Resort, Sardinia, Italy, May 13-15 2010

The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution

Thu, 01 Jul 2010 00:00:00 GMT

The Procesi-Schacher conjecture and Hilbert’s 17th problem for algebras with involution Klep, Igor; Unger, Thomas In 1976 Procesi and Schacher developed an Artin–Schreier type theory for central simple algebras with involution and conjectured that in such an algebra a totally positive element is always a sum of hermitian squares. In this paper elementary counterexamples to this conjecture are constructed and cases are studied where the conjecture does hold. Also, a Positivstellensatz is established for noncommutative polynomials, positive semidefinite on all tuples of matrices of a fixed size.