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We present a new methodology to estimate time varying team strengths of football teams. Our dynamic model allows for deterministic, rather than stochastic, evolution of team strengths. We use the model to identify the best team in England since the English Football Association was formed and match results were recorded in 1888. Our results suggest that Chelsea in 2006 were stronger than any other team has been but that Manchester United have experienced the period of most dominance.

Spline curves, originally developed by numerical analysts for interpolation, are widely used in statistical work, mainly as regression splines and smoothing splines. Barycentric rational interpolants have recently been developed by numerical analysts, but have yet seen very few statistical applications. We give the necesssary information to enable the reader to use barycentric rational interpolants, including a suggestion for a Bayesian prior distribution, and explore the possible statistical use of barycentric interpolants as an alternative to splines. We give the all the necessary formulae, compare the numerical accuracy to splines for some Monte-Carlo datasets, and apply both regression splines and barycentric interpolants to two real datasets. We also discuss the application of these interpolants to data smoothing, where smoothing splines would normally be used, and exemplify the use of smoothing interpolants with another real dataset. Our conclusion is that barycentric interpolants are as accurate as splines, and no more difficult to understand and program. They offer a viable alternative methodology.

Background Laser-Doppler imaging (LDI) of cutaneous blood flow is beginning to be used by burn surgeons to predict the healing time of burn wounds; predicted healing time is used to determine wound treatment as either dressings or surgery. In this paper, we do a statistical analysis of the performance of the technique. Methods We used data from a study carried out by five burn centers: LDI was done once between days 2 to 5 post burn, and healing was assessed at both 14 days and 21 days post burn. Random-effects ordinal logistic regression and other models such as the continuation ratio model were used to model healing-time as a function of the LDI data, and of demographic and wound history variables. Statistical methods were also used to study the false-color palette, which enables the laser-Doppler imager to be used by clinicians as a decision-support tool. Results Overall performance is that diagnoses are over 90% correct. Related questions addressed were what was the best blood flow summary statistic and whether, given the blood flow measurements, demographic and observational variables had any additional predictive power (age, sex, race, % total body surface area burned (%TBSA), site and cause of burn, day of LDI scan, burn center). It was found that mean laser-Doppler flux over a wound area was the best statistic, and that, given the same mean flux, women recover slightly more slowly than men. Further, the likely degradation in predictive performance on moving to a patient group with larger %TBSA than those in the data sample was studied, and shown to be small. Conclusion Modeling healing time is a complex statistical problem, with random effects due to multiple burn areas per individual, and censoring caused by patients missing hospital visits and undergoing surgery. This analysis applies state-of-the art statistical methods such as the bootstrap and permutation tests to a medical problem of topical interest. New medical findings are that age and %TBSA are not important predictors of healing time when the LDI results are known, whereas gender does influence recovery time, even when blood flow is controlled for. The conclusion regarding the palette is that an optimum three-color palette can be chosen 'automatically', but the optimum choice of a 5-color palette cannot be made solely by optimizing the percentage of correct diagnoses.

We present a statistical methodology for fitting time-varying rankings, by estimating the strength parameters of the Plackett–Luce multiple comparisons model at regularly spaced times for each ranked item. We use the little-known method of barycentric rational interpolation to interpolate between the strength parameters so that a competitor's strength can be evaluated at any time. We chose the time-varying strengths to evolve deterministically rather than stochastically, a preference that we reason often has merit. There are many statistical and computational problems to overcome on fitting anything beyond 'toy' data sets. The methodological innovations here include a method for maximizing a likelihood function for many parameters, approximations for modelling tied data and an approach to the elimination of secular drift of the estimated 'strengths'. The methodology has obvious applications to fields such as marketing, although we demonstrate our approach by analysing a large data set of golf tournament results, in search of an answer to the question 'who is the greatest golfer of all time?'

Issue Title: Special Issue on IMA Conference, April 2-4, 2007 - London; Guest Editors: Rose D. Baker, Thierry J. Chaussalet and Martin Utley

A database of failures of many types of medical equipment was analysed, to study the dependence of failure rate on equipment age and on time since repair. The intention was to use this large dataset to assess the validity of some widely-used models of failure rate, such as the power-law and loglinear Poisson processes, and so to recommend simple and adequate models to those practitioners having little data to discriminate between rival models. The aim is also to illustrate a methodology for computing policy costs from failure databases. The power-law process model was found to fit slightly better overall than did the loglinear and linear processes. Some related models were created to fit an observed peaking of failure rate. The data showed a decreasing hazard of (first) failure after repair for some equipment types. This can be due to imperfect or hazardous repair, and also to differing failure rates among a population of machines. Two simple models of imperfect repair were used to fit the data, and an Empirical Bayes method was used to fit a model of variable failure rate between machines. Neglect of such variation can lead to an over-estimate of the hazardousness of repair.

After fitting complex models to data using statistical methods, a sensitivity analysis can be carried out. This determines which parts of a model are causing the bulk of the uncertainty in the model predictions (model \"output\"), and is a decision-support tool for the modeller who contemplates refining a model further or collecting additional data. A simple methodology for carrying out a sensitivity analysis is described. It is envisaged that such a relatively quick insight-generating step would precede the use of a more formal decision-theoretic approach that would address specific questions. Its use is illustrated using a model for breast cancer screening previously published in this journal. A simpler 3-parameter screening model is used in a simulation study of the error of the method as a function of sample size.