PhD and MSc projects with Stephen Senn (MSc / PhD)

Supervisors: Stephen Senn
Relevant research groups: Biostatistics and Statistical Genetics, Statistical Modelling

A list of potential PhD and MSc projects with Stephen Senn can be found at http://www.senns.demon.co.uk/Research.html.

Comparison of methods for conditional quantile estimation (MSc)

Supervisors: Tereza Neocleous
Relevant research groups: Statistical Modelling

Quantile regression (Koenker and Bassett, 1978) is a nonparametricmethod for modelling statistical quantities of interest other than theconditional mean. For instance, to understand how various factors affectlow birth weight one could focus on the lower conditional percentiles(or quantiles) of birth weight given a set of potential predictors.

Generalized Additive Models for Location, Scale and Shape (GAMLSS, Rigbyand Stasinopoulos, 2001 & 2005) fit flexible parametric distributions tothe response variable, and are particularly useful when the responsedoes not follow an exponential family. Both quantile regression andGAMLSS are less restrictive than many commonly used generalized linearmodels, and provide a natural framework for modelling growth curves andbody mass index distributions.

In addition to the above two methods, conditional quantiles could beestimated in a Bayesian nonparametric way by means of Bayesian densityregression (Dunson, Pillai and Park, 2007). The proposed project willcompare the performance of these approaches in a variety of settingsincluding conditional and unconditional growth curve estimation. Theproject is fairly flexible and it can be easily adapted to best suit thestrengths and interests of the prospective student.

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.

Modelling data from brain images (MSc / PhD)

Supervisors: Claire Miller (née Ferguson), Adrian Bowman
Relevant research groups: Statistical Modelling

There is a collaboration underway with the Department of Psychology, who have a full suite of brain imaging equipment.  The current focus is on MEG data, where subjects wear a helmet with embedded electrodes and these pick up signals from the brain over time.  The data are high resolution and quite complex.  The challenge is to use statistical methods to identify the signal from the considerable noise which is present in these experiments.  Current work centres on the use of smoothing techniques to do this.  However, there is very considerable scope for PhD (and MSc) projects in this topic.  There is strong support and interest from the Department of Psychology.

Modelling three-dimensional shape data (MSc / PhD)

Supervisors: Adrian Bowman
Relevant research groups: Statistical Modelling

Modern imaging equipment provides very interesting forms of data.  This project focusses on a stereo camera system which is able to construct a three-dimensional model of the surface of an object.  There are many clinical applications of this.  A longstanding one is in the analysis of facial shape of those who have undergone surgery for conditions such as cleft lip and palate.  More recently attention has shifted to quantifying the effects of surgical operations in adult faces.  Analysis of the data raises very interesting questions about how to measure shape and shape change.  One research students and one research assistant are already working on these topics but there are quite a few possibilities for further student projects, as part of this small team.

Spatiotemporal modelling of hydrological catchments (PhD)

Supervisors: Claire Miller (née Ferguson), Marian Scott OBE, Adrian Bowman
Relevant research groups: Environmental Statistics, Statistical Modelling

Regulatory bodies, such as the Environment Agency of England and Wales and the Scottish Environment Protection Agency, regularly monitor river surface water. The purpose of this is to assess the levels of nutrients etc. in the water to report levels to Europe and also to address how to reduce such levels, if necessary, to meet European standards.

River monitoring locations are contained in small waterbodies, which are the standard surface water reporting units for the Water Framework Directive (WFD, European Parliament; 2000). A collection of waterbodies, covering a river network, are contained in a large hydrological area (LHA), and each LHA contains an independent river network. This project will develop spatiotemporal hierarchical models for such data incorporating different levels of spatial correlation within and between catchments and contributory catchment information.

There are several statistical challenges associated with such modelling including incorporating space-time interactions and space-time covariance structures. The overall data dimensionality for such problems is large. However, at particular monitoring locations data can be sparse in space and/or time. Monitoring locations along rivers are flow-connected with models requiring catchment information and river network covariance structures.