On perfect simulation for some mixtures of distributions

This paper studies the implementation of the coupling from the past (CFTP) method of Propp and Wilson (1996) in the set-up of two and three component mixtures with known components and unknown weights. We show that monotonicity structures can be exhibited in both cases, but that CFTP can still be costly for three component mixtures. We conclude with a simulation experiment exhibiting an almost perfect sampling scheme where we only consider a subset of the exhaustive set of starting values.     

Using quantile averages in matched observational studies

In two observational studies, one investigating the effects of minimum wage laws on employment and the other of the effects of exposures to lead, an estimated treatment effect's sensitivity to hidden bias is examined. The estimate uses the combined quantile averages that were introduced in 1981 by B. M. Brown as simple, efficient, robust estimates of location admitting both exact and approximate confidence intervals and significance tests. Closely related to Gastwirth's estimate and Tukey's trimean, the combined quantile average has asymptotic efficiency for normal data that is comparable with that of a 15% trimmed mean, and higher efficiency than the trimean, but it has resistance to extreme observations or breakdown comparable with that of the trimean and better than the 15% trimmed mean. Combined quantile averages provide consistent estimates of an additive treatment effect in a matched randomized experiment. Sensitivity analyses are discussed for combined quantile averages when used in a matched observational study in which treatments are not randomly assigned. In a sensitivity analysis in an observational study, subjects are assumed to differ with respect to an unobserved covariate that was not adequately controlled by the matching, so that treatments are assigned within pairs with probabilities that are unequal and unknown. The sensitivity analysis proposed here uses significance levels, point estimates and confidence intervals based on combined quantile averages and examines how these inferences change under a range of assumptions about biases due to an unobserved covariate. The procedures are applied in the studies of minimum wage laws and exposures to lead. The first example is also used to illustrate sensitivity analysis with an instrumental variable.     

Detecting a changed segment in DNA sequences

Non-coding deoxyribonucleic acid (DNA) can typically be modelled by a sequence of Bernoulli random variables by coding one base, e.g. T, as 1 and other bases as 0. If a segment of a sequence is functionally important, the probability of a 1 will be different in this changed segment from that in the surrounding DNA. It is important to be able to see whether such a segment occurs in a particular DNA sequence and to pin-point it so that a molecular biologist can investigate its possible function. Here we discuss methods for testing the occurrence of such a changed segment and how to estimate the end points of it. Maximum-likelihood-based methods are not very tractable and so a nonparametric method based on the approach of Pettitt has been developed. The problem and its solution are illustrated by a specific DNA example.     

The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology

For frequency counts, the situation of extra zeros often arises in biomedical applications. This is demonstrated with count data from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Extra zeros, however, violate the variance–mean relationship of the Poisson error structure. This extra-Poisson variation can easily be explained by a special mixture model, the zero-inflated Poisson (ZIP) model. On the basis of the ZIP model, a graphical device is presented which not only summarizes the mixing distribution but also provides visual information about the overall mean. This device can be exploited to evaluate and compare various groups. Ways are discussed to include covariates and to develop an extension of the conventional Poisson regression. Finally, a method to evaluate intervention effects on the basis of the ZIP regression model is described and applied to the data of the Belo Horizonte caries prevention study.     

Forecasting on British election night 1997

An account is given of methods used to predict the outcome of the 1997 general election from early declared results, for use by the British Broadcasting Corporation (BBC) in its election night television and radio coverage. Particular features of the 1997 election include extensive changes to constituency boundaries, simultaneous local elections in many districts and strong tactical voting. A new technique is developed, designed to eliminate systematic sources of bias such as differential refusal, for incorporating prior information from the BBC's exit poll. The sequence of forecasts generated on election night is displayed, with commentary.     

Prior distribution assessment for a multivariate normal distribution: an experimental study

A variety of methods of eliciting a prior distribution for a multivariate normal (MVN) distribution have recently been proposed. This paper reports an experiment in which 16 meteorologists used the methods to quantify their opinions about climatology variables. Our results compare prior models and show, in particular, that it can be better to assume the mean and variance of an MVN distribution are independent a priori, rather than to model opinion by the conjugate prior distribution. Using a proper scoring rule, different forms of assessment task are examined and alternative ways of estimating parameters are compared. To quantify opinion about means, it proved preferable to ask directly about the means rather than individual observations while, to quantify opinion about the variance matrix, it was best to ask about deviations from the mean. Further results include recommendations for the way parameters of the prior distribution are estimated.     

SPC—a team effort for process improvement across four Area Control Centres

This paper describes an innovative application of statistical process control to the online remote control of the UK's gas transportation networks. The gas industry went through a number of changes in ownership, regulation, access to networks, organization and management culture in the 1990s. The application of SPC was motivated by these changes along with the desire to apply the best industrial statistics theory to practical problems. The work was initiated by a studentship, with the technology gradually being transferred to the industry. The combined efforts of control engineers and statisticians helped develop a novel SPC system. Having set up the control limits, a system was devised to automatically update and publish the control charts on a daily basis. The charts and an associated discussion forum are available to both managers and control engineers throughout the country at their desktop PCs. The paper describes methods of involving people to design first-class systems to achieve continual process improvement. It describes how the traditional benefits of SPC can be realized in a 'distal team working', and 'soft systems', context of four Area Control Centres, controlling a system delivering two thirds of the UK's energy needs.     

Predicting distances using a linear model: the case of varietal distinctness

Differences between plant varieties are based on phenotypic observations, which are both space and time consuming. Moreover, the phenotypic data result from the combined effects of genotype and environment. On the contrary, molecular data are easier to obtain and give a direct access to the genotype. In order to save experimental trials and to concentrate efforts on the relevant comparisons between varieties, the relationship between phenotypic and genetic distances is studied. It appears that the classical genetic distances based on molecular data are not appropriate for predicting phenotypic distances. In the linear model framework, we define a new pseudo genetic distance, which is a prediction of the phenotypic one. The distribution of this distance given the pseudo genetic distance is established. Statistical properties of the predicted distance are derived when the parameters of the model are either given or estimated. We finally apply these results to distinguishing between 144 maize lines. This case study is very satisfactory because the use of anonymous molecular markers (RFLP) leads to saving 29% of the trials with an acceptable error risk. These results need to be confirmed on other varieties and species and would certainly be improved by using genes coding for phenotypic traits.     

The quincunx: history and mathematics

Received: December 30, 1999; revised version: July 19, 2000     

Modelling change in cognitive understanding with finite mixtures

Psychological theories often posit the existence of several different states. Individuals are viewed as belonging to one of the states at a given age, but with development pass to another state. A main problem in evaluating such theories is representing the transition from one state to another over age. A stochastic transition framework is proposed which should be useful in many different settings. The model is illustrated with data from a cognitive development task.