Statistics Postgraduate Talks III
Thursday 25th July, 2013 14:00-16:20 Maths 203
Spatio-temporal modelling of large hydrological catchments - Kelly Gallacher (2pm)
Several statistical methods exist that can be used to model trends and seasonality in spatiotemporal data sets. The seasonal pattern of log(TON) for a single hydrological area in Wales was estimated using four statisti- cal methods (Additive models, Dynamic Factor Analysis, Functional Data Analysis and INLA) and a novel approach to comparing these estimates has been developed. The comparison is based on a measure of distance be- tween curves that aims to measure distance as it would be judged ‘by eye’, an adaptation of a hypothesis test originally developed for use in genetics applications and curvature. The hypothesis test shows that the estimated seasonal patterns are significantly different. The estimated curves differ in terms of the day of year at which minimum log(TON) occurs and magnitude of curvature at this point. Each model incorporates spatial structure in a different way which might account for differences between estimates.
Vinny Davies (2.20pm)
In transcriptional regulation, transcription factors (TFs) are often unobservable at mRNA level or may be controlled outside of the system being modelled. Gaussian processes are a promising approach for dealing with these difficulties as a prior distribution can be defined over the latent TF activity profiles and the posterior distribution inferred from the observed expression levels of potential target genes. However previous approaches have been based on the assumption of additive Gaussian noise to maintain analytical tractability. We investigate the influence of a more realistic form of noise on a biologically accurate system based on Michaelis-Menten kinetics
Parameter inference in complex biological systems using adaptive gradient matching with Gaussian processes and parallel tempering - Benn Macdonald (2.40pm)
Parameter inference in mathematical models of complex biological systems, expressed as coupled ordinary differential equations (ODEs), is a chal- lenging problem. The systems depend on chemical kinetic parameters, which usually cannot all be measured and must be inferred from the data. Conven- tional methods using Markov Chain Monte Carlo (MCMC) sampling tend to involve integrating the system of ODEs at each iterative step, to see how well the sampled parameters correspond with the data. However, the computational costs associated with repeatedly solving the ODEs are often staggering, making many techniques impractical. Therefore, aimed at reducing this cost, new con- cepts using gradient matching have been proposed. These approaches generally work by first smoothing the signal (to avoid modelling the observational noise), then comparing the gradients from the resulting interpolant with those predicted from the ODEs. My work, using a Bayesian approach, combines current adap- tive gradient matching (AGM) techniques, using Gaussian process interpolation, with a parallel tempering scheme. The AGM allows the sampled parameters of the ODEs to reshape the interpolant, proceeding to less mismatch between the gradients. As well as tempering the posterior across parallel MCMC chains, I also temper the mismatch hyperparameter that governs the difference between the gradients. In this way, it is possible to have the gradients from our interpolant closely match those from the ODEs, for chains closer to the target posterior. I use 2 ODE systems to assess my new technique: a simple model depicting neuron firing (Fitz-Hugh Nagumo) and a model of the behaviour of autocatalytic reac- tions (Lotka-Volterra). An application to protein signal transduction pathways is also examined. Presented is a comparative evaluation with other methods that are representative of the current state of the art.
Facial Shape Analysis - Liberty Vittert (3pm)
Having compared many different methodological tools to analyze the collected control data and (pre/post) facial reconstructed patient data, a variant on Fisher's method has been used to analyze the differences in facial shape between males and females, shape change with age, and the differences between control cases and facially reconstructed cases.
Longitudinal Study of Facial Growth in Childhood - Anna Price (3.20pm)
In the field of statistical facial shape analysis, much research has focused on 2-dimensional data. However, there has been considerably less work carried out on 3-dimensional images. An understanding of facial shape and growth can aid in the planning and evaluation of facial surgery for children with cleft lip and palate. Therefore it is of interest to establish a standard model from control data that allows comparisons to be made. This project has involved the follow-up of a longitudinal study of control children and the development of an automatic facial curve identification algorithm which can be used to analyse the longitudinal data.
Comparison of the performance of methods of constructing growth charts - Elizabeth Irwin (3.40pm)
People are interested in monitoring growth in many fields. Growth charts illustrate typical growth patterns, describing how a physical characteristic changes with age for a certain population. They are constructed on a reference population which contains a representative sample of individuals from this population, whose physical characteristic measurement may have been observed at multiple ages. My research is primarily focusing on growth charts constructed for infants' weight measurements, which depict reference centile curves illustrating how infants' weights changes between birth and roughly two years of age. The LMS and QR approaches have been used for estimating these growth charts.