Professor Charles Taylor
With rapid advances in technology, and increasing ease of data capture and storage, there will be many challenges and opportunites for Statisticians for many years to come.
- Head of Statistics
Statistical Learning and Data Mining
Density estimation is a key area within nonparametric statistics which is used in exploratory data analysis and the formulation of hypotheses. A critical choice for user interpretation is how much smoothing to use. In this context I have made innovative utilization of three automatic procedures for three methods of estimation: Akaike's Information Criterion to determine the class width of the histogram, cross-validation methods to choose the number of terms in an orthogonal series estimator, and the bootstrap to choose the window width in the kernel estimator. The latter paper, in particular, is highly regarded since analytical calculations can be used to calculate the ootstrap expectations thus avoiding the usual recourse to simulation. My current interests lie in: the application of kernel density estimation to discrimination problems; the effect of enhancing classifiers through boosting and bagging, and adaptation of kernel methods to circular data.
Data Mining (which provides tools for turning large databases into knowledge) is widely seen as increasingly important topic, particularly with the ability to automatically collect, and store large amounts of data. This field is being tackled by both computer scientists and, to a lesser extent, by statisticians. I have played a key role in cross-fertilization of methods, performance indicators, and formulation of further key issues to resolve.
Spatial statistics and image analysis
Over the past twenty years, statistical methods have gained an increasing role in image analysis and the analysis of spatial data. I have made a significant contribution in
- Image summaries, which are important for identifying suitable models and for classification on the basis of the extracted features. These features can be measurable physical quantities of objects in an image (for example the ratio height/width can be useful in identifying the number 1 in the automatic recognition of vehicle number plates) or they can be parameters in a statistical model (for example the variance).
With the advent of increasing amounts of resolution, it has become possible to estimate the fractal dimension of objects (or their outline) in an image. The fractal dimension is another example of an image summary which can be used to describe objects, and to classify future observations. In this context, I have made a contribution to methods of its estimation (Taylor & Taylor, 1991).
Frequently, single number summaries are inadequate, and (univariate) functions are used to describe features of the image. For example, in a point pattern the density of the distance between two randomly chosen pairs of points can be used to describe clustering or inhibitions - for example, for species which are in competition. For point patterns which are highly regular, the usual sequential methods of simulation are prohibitively slow and I (together with Ian Dryden) have developed several innovative methods for a new model. These methods include a Procrustes shape analysis, and an analysis of interpoint distances based on size. In addition, I have developed methods which have been successfully used for discrimination on the basis of morphological summaries.
In 2017-18 I will teach MATH5741 Statistical Theory and Methods, and organize the MSc dissertations for students taking Statistics, Statistics with Applications to Finance, and Data Science and Analytics (MATH5871, and MATH5872)
Research groups and institutes