A wavelet approach to shape analysis for spinal curves

We present a new method to describe shape change and shape differences in curves, by constructing a deformation function in terms of a wavelet decomposition. Wavelets form an orthonormal basis which allows representations at multiple resolutions. The deformation function is estimated, in a fully Bayesian framework, using a Markov chain Monte Carlo algorithm. This Bayesian formulation incorporates prior information about the wavelets and the deformation function. The flexibility of the MCMC approach allows estimation of complex but clinically important summary statistics, such as curvature in our case, as well as estimates of deformation functions with variance estimates, and allows thorough investigation of the posterior distribution. This work is motivated by multi-disciplinary research involving a large-scale longitudinal study of idiopathic scoliosis in UK children. This paper provides novel statistical tools to study this spinal deformity, from which 5% of UK children suffer. Using the data we consider statistical inference for shape differences between normals, scoliotics and developers of scoliosis, in particular for spinal curvature, and look at longitudinal deformations to describe shape changes with time.     

On adaptive estimation

Point estimates that are weighted averages of other estimates are considered. They are adaptive because the weights are also functions of the sample observations.In particular, the weights are functions of new measures of peakedness and skewness. Five adaptive estimators are compared (in a Monte Carlo study using the swindle) to some of the usual estimators, including those robust ones of Huber and Tukey. In addition, the swindle constant is considered in some detail. All of the adaptive estimators do extremely well with an adaptive biweight statistic being the best one in this study. Suggestions are made about future directions in this area.     

Construction and evaluation of matched quick switching systems

This paper presents a method and set of tables for the selection of equivalent basic single-sampling plans (without switching rules) and a quick switching system which includes switching rules. A better pe florming system is identifed and is compared with a sampling system which uses the switching rules ofMIL-STD-lO5D.     

On statistical problems with face identification from photographs

SUMMARY Automatic identification of faces from a database given a digital view is becoming increasingly important. The question arises whether or not there can be a face identification system similar to the fingerprinting system, where a certain number of matches are regarded as sufficient to identify the person in the database. We first give a very general review of the topic of facial measurements and indicate some deep statistical problems. We then analyze a database of photographs. Certain characteristics of the population are provided, such as the modes of variation and correlation structures using shape analysis. The data involve angles as well as distances. The principal component analysis for angular data is discussed, its conversion into landmark data is established and the two approaches are compared. A new approach of anchor shape analysis for specialized distances is discussed.     

Sampling systems indexed by the crossover point

This paper presents the designing methodology for the quick switching system, indexed by an entry parameter called the 'crossover point' (COP). The significance of the COP and the properties of the operating characteristic curve with respect to the COP are studied and the necesssary tables constructed.