Charles C. Taylor

A generative, probabilistic model of local protein structure

Despite significant progress in recent years, protein structure prediction maintains its status as one of the prime unsolved problems in computational biology. One of the key remaining challenges is an efficient probabilistic exploration of the structural space that correctly reflects the relative conformational stabilities. Here, we present a fully probabilistic, continuous model of local protein structure in atomic detail. The generative model makes efficient conformational sampling possible and provides a framework for the rigorous analysis of local sequence–structure correlations in the native state. Our method represents a significant theoretical and practical improvement over the widely used fragment assembly technique by avoiding the drawbacks associated with a discrete and nonprobabilistic approach.

Machine learning and statistics: the interface

Statistical Properties of Tree-Based Approaches to Classification The Decision Tree Algorithm CAL5 Based on a Statistical Approach to its Splitting Algorithm Probabilistic Symbolic Classifiers: An Empirical Comparison from a Statistical Perspective A Multistrategy Approach to Learning Multiple Dependent Concepts Quality of Decision Rules - Definition and Classification Schemes for Multiple Rules DIPOL - A Hybrid Piecewise Linear Classifier Combining Classification Procedures Distance-based Decision Trees Learning Fuzzy Controllers from Examples Some Developments in Statistical Credit Scoring Combination of Statistical and Other Learning Methods to Predict Financial Time Series.

Bayesian texture segmentation of weed and crop images using reversible jump Markov chain Monte Carlo methods

A Bayesian method for segmenting weed and crop textures is described and implemented. The work forms part of a project to identify weeds and crops in images so that selective crop spraying can be carried out. An image is subdivided into blocks and each block is modelled as a single texture. The number of different textures in the image is assumed unknown. A hierarchical Bayesian procedure is used where the texture labels have a Potts model (colour Ising Markov random field) prior and the pixels within a block are distributed according to a Gaussian Markov random field, with the parameters dependent on the type of texture. We simulate from the posterior distribution by using a reversible jump Metropolis-Hastings algorithm, where the number of different texture components is allowed to vary. The methodology is applied to a simulated image and then we carry out texture segmentation on the weed and crop images that motivated the work. Copyright 2003 Royal Statistical Society.

Kernel density classification and boosting: an L2 analysis

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification.A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research.

Assessment of cooked alpaca and llama meats from the statistical analysis of data collected using an 'electronic nose'.

As part of an EU-funded project to assist in developing the production chain of meat from camelids in South America we have investigated the possibility of using an electronic nose to distinguish between the different types of meat of commercial interest. On-site monitoring of freshly cooked camelid meat using a Bloodhound electronic nose has been carried out in Peru and Bolivia. Sampling was carried out using inert, collapsible plastic bags. Linear discriminant analysis of data generated by the electronic nose classified the samples of meat. Some problems experienced in analysing the data relating to sample size are discussed.

Nonparametric Regression for Spherical Data

We develop nonparametric smoothing for regression when both the predictor and the response variables are defined on a sphere of whatever dimension. A local polynomial fitting approach is pursued, which retains all the advantages in terms of rate optimality, interpretability, and ease of implementation widely observed in the standard setting. Our estimates have a multi-output nature, meaning that each coordinate is separately estimated, within a scheme of a regression with a linear response. The main properties include linearity and rotational equivariance. This research has been motivated by the fact that very few models describe this kind of regression. Such current methods are surely not widely employable since they have a parametric nature, and also require the same dimensionality for prediction and response spaces, along with nonrandom design. Our approach does not suffer these limitations. Real-data case studies and simulation experiments are used to illustrate the effectiveness of the method.

Image segmentation using voronoi polygons and MCMC, with application to muscle fibre images

Abstract We investigate a Bayesian method for the segmentation of muscle fibre images. The images are reasonably well approximated by a Dirichlet tessellation, and so we use a deformable template model based on Voronoi polygons to represent the segmented image. We consider various prior distributions for the parameters and suggest an appropriate likelihood. Following the Bayesian paradigm, the mathematical form for the posterior distribution is obtained (up to an integrating constant). We introduce a Metropolis–Hastings algorithm and a reversible jump Markov chain Monte Carlo algorithm (RJMCMC) for simulation from the posterior when the number of polygons is fixed or unknown. The particular moves in the RJMCMC algorithm are birth, death and position/colour changes of the point process which determines the location of the polygons. Segmentation of the true image was carried out using the estimated posterior mode and posterior mean. A simulation study is presented which is helpful for tuning the hyperparameters and to assess the accuracy. The algorithms work well on a real image of a muscle fibre cross-section image, and an additional parameter, which models the boundaries of the muscle fibres, is included in the final model.

Mixtures of concentrated multivariate sine distributions with applications to bioinformatics

Motivated by examples in protein bioinformatics, we study a mixture model of multivariate angular distributions. The distribution treated here (multivariate sine distribution) is a multivariate extension of the well-known von Mises distribution on the circle. The density of the sine distribution has an intractable normalizing constant and here we propose to replace it in the concentrated case by a simple approximation. We study the EM algorithm for this distribution and apply it to a practical example from protein bioinformatics.

A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics

Efron (1979) introduced the bootstrap method for independent data but it cannot be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is related to the block size which is difficult to select. In the moving block bootstrap method also the variance estimator is underestimated. In this paper, first the semi-parametric bootstrap is used to estimate the precision measures of estimators in spatial data analysis. In the semi-parametric bootstrap method, we use the estimation of the spatial correlation structure. Then, we compare the semi-parametric bootstrap with a moving block bootstrap for variance estimation of estimators in a simulation study. Finally, we use the semi-parametric bootstrap to analyze the coal-ash data.

Hierarchical Bayesian modelling of spatial age-dependent mortality

Hierarchical Bayesian modelling is considered for the number of age-dependent deaths in different geographic regions. The model uses a conditional binomial distribution for the number of age-dependent deaths, a new family of zero mean Gaussian Markov random field models for incorporating spatial correlations between neighbouring regions, and an intrinsic Gaussian model for including correlations between age-dependent mortality rates. Age-dependent mortality rates are estimated for each region, and approximate credibility intervals based on summaries of samples from the posterior distribution are obtained from Markov chain Monte Carlo simulation. The consequent maps of mortality rates are less variable and smoother than those which would be obtained from naive estimates, and various inferences may be drawn from the results. The prior spatial model includes some of the common conditional autoregressive spatial models used in epidemiology, and so model uncertainty in this family can be accounted for. The methodology is illustrated with an actuarial data set of age-dependent deaths in 150 geographic regions of Hungary. Sensitivity to the prior distributions is discussed, as well as relative risks for certain covariates (males in towns, females in towns, males in villages, females in villages).