The evolution of shape (MSc / PhD)

Supervisors: Vincent Macaulay
Relevant research groups: Computational Statistics and Inference, Biostatistics and Statistical Genetics

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.

Interactive representations of uncertainty for modern statistical inference (PhD)

Relevant research groups: Statistical Modelling, Computational Statistics and Inference

In many scientific areas the exploration of the uncertainty of parameters or quantities of interest is as important as estimating the individual effects. A careful assessment of uncertainty using statistical modelling lends support to a scientific analysis. But such assessments can be limited by the use of static summaries for data and statistical model parameters, which cannot capture the space of variations or the sensitivity of model elements to change. Interactive exploration of uncertainty, while more computationally intensive, can afford investigation of otherwise difficult-to-perceive interactions and relationships between quantities of interest, and can generate new scientific hypotheses. This Ph.D. project will propose and investigate methods for effective interactive exploration of uncertainty in data and statistical model output suited to large sensor networks.

Candidates should have an excellent single or combined degree in Statistics or Computing Science and have strong computational and mathematical modelling skills. Excellent written and oral communication skills, and strong time-management skills are also desirable.

The College of Science and Engineering at the University of Glasgow is investing in interdisciplinary research on sensors and sensor systems. This exciting project will be co-supervised by academics from the Schools of Computing Science, and Mathematics and Statistics.

The studentship covers fees and a stipend (at UK and EU student levels). The stipend is based on the UK Research Council rates and the studentship will be of 3.5 years duration.

Closing date: Monday 20th May 2013
Expected start date: 1st October 2013

For further information, please contact
Dr. Peter Craigmile (peter.craigmile@glasgow.ac.uk) or
Dr. John Williamson (jhw@dcs.gla.ac.uk)

Bayesian variable selection for genetic and genomic studies (PhD)

Supervisors: Mayetri Gupta
Relevant research groups: Computational Statistics and Inference

An important issue in high-dimensional regression problems is the accurate and efficient estimation of regression coefficients when, compared to the number of data points, a substantially larger number of potential predictors are present. A further complication arises with correlated predictors, leading to the breakdown of standard statistical models for inference. Examples of such problems arise in many scenarios- in determining expression patterns of genes that may be responsible for a type of cancer; and in determining which genetic mutations lead to higher risks for occurrence of a disease. This project involves developing broad and improved Bayesian methodologies for efficient inference in high-dimensional regression-type problems, with a focus on genetic data applications. Further, we will extend this framework to a variety of latent class models, and investigate the operating characteristics and analytical properties of various priors in the context of variable selection.

Clustering methods to detect genetic associations (PhD)

Supervisors: Mayetri Gupta
Relevant research groups: Biostatistics and Statistical Genetics, Computational Statistics and Inference

Many common diseases including cardiovascular disease and osteoporosis are characterized by complex traits, which are determined by the interplay of numerous genetic variants and various environmental factors. Although genetic and phenotypic data may contain the information to decipher complex diseases, building global models that can associate complex traits with the appropriate genetic profile leads to several formidable statistical and computational challenges. Model-based methods for clustering provide a promising approach, but are generally difficult to implement here due to unknown numbers of clusters and a lack of a grouping structure in a large part of the data. This project aims to develop a Bayesian model-based framework and methodologies for clustering blocks of SNPs and phenotypes that can identify sets of candidate genes associated with traits for different diseases. In the scientific context, it is becoming increasingly important to understand the biological system as a whole, taking into account heterogeneity between populations and individuals, simultaneously with  individual-level genome-specific biological characteristics. A longer-term goal would be to develop efficient methods for detecting associations incorporating genomic function with genetic variability.

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