Statistical Methodology
The work done by this group involves the development of generic statistical methodology. Although it would be hoped that the research would be of great value in real applications, most of the work either is not motivated by a particular application area or is motivated by one applied field but with the potential for use in other areas as well. Bayesian and non-Bayesian approaches are taken and much of the work is of a computational flavour, in line with modern trends in the subject.
Dr Nema Dean Lecturer
Supervised and unsupervised learning; mixture models; variable selection; microarray data analysis
Research students: Craig Anderson, Stephen Rowley
Dr Ludger Evers Lecturer
Statistical methods in machine learning; partition and mixture-based models; non-linear dimension reduction; microarray data analysis
Member of other research groups: Statistical Modelling, Scholarship of Learning and Teaching in Statistics
Research students: Charalampos Chanialidis, Rob Donald, Daniel Molinari, Stephen Rowley
Postgraduate opportunities: Mixture-based approaches to quantile regression, Quantile regression for count data
Prof Dirk Husmeier Chair of Statistics, Group Leader
Machine learning and Bayesian statistics applied to systems biology and bioinformatics; Bayesian networks; statistical phylogenetics
Member of other research groups: Statistical Modelling
Research staff: Ruirui Ji
Research students: Andreij Aderhold (U of St Andrews), Frank Dondelinger (BioSS / U of Edinburgh)
Dr Ruirui Ji Visiting Research Assisstant
Gaussian processes for machine learning; gene regulation models; microarray data analysis
Supervisor: Dirk Husmeier
Dr Vincent Macaulay Senior Lecturer
Statistical genetics; population genetics; Bayesian methods; phylogenetics
Member of other research groups: Biostatistics and Statistical Genetics
Research students: Mhairi Kerr, Colette Mair
Postgraduate opportunities: The evolution of shape, Modelling Genetic Variation
Dr Agostino Nobile Lecturer
Bayesian statistics; MCMC and other Monte Carlo methods; mixture models; discrete choice models
Research students: George Cairns, Gary Napier
Prof Michael Titterington Emeritus Professor
Statistical analysis of mixture distributions; latent structure analysis; pattern recognition; machine learning; smoothing and nonparametric statistics; optimum design of experiments
Research student: George Cairns
Dr Bernard Torsney Senior Lecturer
Non-parametric inference; optimisation; optimal experimental design; sampling theory; applications in economics; multiple comparisons
Postgraduate opportunities: Latent Models for Ranking Studies: developing, fitting and designing for
Charalampos Chanialidis PhD Student
Research Topic: Bayesian mixture models for quantile regression
Member of other research groups: Statistical Modelling
Supervisors: Ludger Evers, Tereza Neocleous
Collette Letham MSc Student
Research Topic: Documenting and imputing missing values in a longitudinal survey of students' personal attributes
Supervisor: John McColl
Stephen Rowley MSc Student
Research Topic: Sampling algorithms for hierarchical mixture of experts
Supervisors: Nema Dean, Ludger Evers
Quantile regression for count data (PhD)
Supervisors: Ludger Evers, Tereza Neocleous
Relevant research groups: Statistical Modelling, Statistical Methodology
Quantile regression provides a framework for modelling statisticalquantities of interest other than the conditional mean as often one ismore interested in the entire conditional distribution of the responsevariable rather than the conditional mean. Quantile regression hasapplications in many fields including environmetrics, economics andpublic health. In these disciplines the data collected are often counts,rather than continuous outcomes. Whilst the quantile regression methodology is well developed for continuous outcomes, only few modelsexist for count data. One approach to quantile regression for count datais that by Machado and Santos Silva (2005) who add uniform random noiseto the count data. This approach is popular in economics and ecologyapplications.
We propose to develop a Bayesian model for quantile regression for countdata based on adaptive mixtures of generalisations of the Poissondistribution. This approach has the advantage of not only being fullyflexible but also being "centred" around a standard distribution forcount data. Thus we hope to be able to use simple models with only fewmixture components. Similar approaches have been in use in the MachineLearning community ("Mixtures of experts", see e.g. Jordan and Jacob,1994) and more recently in the area of Bayesian quantile regression forcontinuous data (see e.g. Dunson et al. 2007).
Mixture-based approaches to quantile regression (PhD)
Supervisors: Tereza Neocleous, Ludger Evers
Relevant research groups: Statistical Modelling, Statistical Methodology
Quantile regression provides a framework for modelling statisticalquantities of interest other than the conditional mean. For instance, tounderstand how various factors affect low birth weight one could focuson the lower conditional percentiles (or quantiles) of birth weightgiven a set of potential predictors. Quantile regression hasapplications in a wide range of fields such as environmetrics, economicsand public health.
Approaches based on mixture distributions (such as mixtures ofGaussians) and related concepts like the Dirichlet process and the Polyaprocess have been used successfully in Bayesian nonparametrics.Recently, some of these methods have been extended to allow includingcovariates in the model (e.g. Dunson, Pillai and Park, 2007). Thisallows using them as Bayesian quantile regression methods.
The proposed project involves both the implementation of sophisticatedstatistical algorithms as well as their application to real-world data.In addition to providing insight into an exciting and very activestatistical research area, the project also offers the opportunity toparticipate in the development of novel statistical methods. Due to thebreadth of the topic and the flexibility of the project it can easily beadapted to best suit the strengths and interests of the prospectivestudent.
Latent Models for Ranking Studies: developing, fitting and designing for (MSc)
Supervisors: Bernard Torsney
Relevant research groups: Statistical Methodology
The evolution of shape (PhD)
Supervisors: Vincent Macaulay
Relevant research groups: Statistical Methodology
Shapes of objects change in time. Organisms evolve and in the process change form: humans and chimpanzees derive from some common ancestor presumably different from either in shape. Designed objects are no different: an Art Deco tea pot from the 1920s might share some features with one from Ikea in 2010, but they are different. Mathematical models of evolution for certain data types, like the strings of As, Gs , Cs and Ts in our evolving DNA, are quite mature and allow us to learn about the relationships of the objects (their phylogeny or family tree), about the changes that happen to them in time (the evolutionary process) and about the ways objects were configured in the past (the ancestral states), by statistical techniques like phylogenetic analysis. Such techniques for shape data are still in their infancy. This project will develop novel statistical inference approaches (in a Bayesian context) for complex data objects, like functions, surfaces and shapes, using Gaussian-process models, with potential application in fields as diverse as language evolution, morphometrics and industrial design.
