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.     

Estimating the frequency of familial dilated cardiomyopathy in the presence of misclassification errors

Dilated cardiomyopathy is a disease of unknown cause characterized by dilation and impaired function of one or both ventricles. Most cases are believed to be sporadic, although familial forms have been detected. The familial form has been estimated to have a relative frequency of about 25%. Since, except for familial history, familial form has no other characteristics that could help in classifying the two diseases, the estimate of the frequency of the familial form should take into account a possible misclassification error. In our study, 100 cases were randomly selected in a prospective series of 350 patients. Out of them, 28 index cases were included in the analysis: 12 were known to be familial, and 88 were believed to be sporadic. After extensive clinical examination of the relatives, 3 patients supposed to have a sporadic form were found to have a familial form. 13 cases had a confirmed sporadic disease. Models in the Log-Linear Product class (LLP) have been used to separate classification errors from underlying patterns of disease incidence. The most conservative crude estimate of the misclassification error is 16.1% (CI 0.22- 23.27%), which leads to a crude estimate of the frequency of the familiar form of about 60%. An estimate of the disease frequency, adjusted for taking into consideration the sampling plan, is 40.93% (CI 32.29-44.17%). The results are consistent with the hypothesis that genetic factors are still underestimated, although they represent a major cause of the disease.     

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.     

Data-based interval estimation of classification error rates

Leave-one-out and 632 bootstrap are popular data-based methods of estimating the true error rate of a classification rule, but practical applications almost exclusively quote only point estimates. Interval estimation would provide better assessment of the future performance of the rule, but little has been published on this topic. We first review general-purpose jackknife and bootstrap methodology that can be used in conjunction with leave-one-out estimates to provide prediction intervals for true error rates of classification rules. Monte Carlo simulation is then used to investigate coverage rates of the resulting intervals for normal data, but the results are disappointing; standard intervals show considerable overinclusion, intervals based on Edgeworth approximations or random weighting do not perform well, and while a bootstrap approach provides intervals with coverage rates closer to the nominal ones there is still marked underinclusion. We then turn to intervals constructed from 632 bootstrap estimates, and show that much better results are obtained. Although there is now some overinclusion, particularly for large training samples, the actual coverage rates are sufficiently close to the nominal rates for the method to be recommended. An application to real data illustrates the considerable variability that can arise in practical estimation of error rates.     

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.     

Adaptive Estimation Using Weighted Least Squares

This paper proposes an adaptive estimator that is more precise than the ordinary least squares estimator if the distribution of random errors is skewed or has long tails. The adaptive estimates are computed using a weighted least squares approach with weights based on the lengths of the tails of the distribution of residuals. Smaller weights are assigned to those observations that have residuals in the tails of long-tailed distributions and larger weights are assigned to observations having residuals in the tails of short-tailed distributions. Monte Carlo methods are used to compare the performance of the proposed estimator and the performance of the ordinary least squares estimator. The estimates that were studied in this simulation include the difference between the means of two populations, the mean of a symmetric distribution, and the slope of a regression line. The adaptive estimators are shown to have lower mean squared errors than those for the ordinary least squares estimators for short-tailed, long-tailed, and skewed distributions, provided the sample size is at least 20. The ordinary least squares estimator has slightly lower mean squared error for normally distributed errors. The adaptive estimator is recommended for general use for studies having sample sizes of at least 20 observations unless the random errors are known to be normally distributed.     

Recovering Information from Incremental Responses

Some yields analysed and reported in the literature have been adjusted by subtracting a control. It is found that full information can be recovered for estimable parameters and the error variance using these incremental responses, in comparison with unadjusted data. These findings are of practical importance, and they supplement materials usually found in a graduate course in linear inference. The issues are illustrated using a case study from the literature.     

Markov Chains and De-initializing Processes

We define a notion of de-initializing Markov chains. We prove that to analyse convergence of Markov chains to stationarity, it suffices to analyse convergence of a de-initializing chain. Applications are given to Markov chain Monte Carlo algorithms and to convergence diagnostics.     

The cluster that never was: germ warfare experiments and health authority reality in Dorset

In 1997 intense media coverage raised public concerns about germ warfare simulation experiments conducted by the Ministry of Defence during the 1960s, which included the release of bacteria over Dorset. Families in East Lulworth, Dorset, have linked this with allegedly high rates of miscarriages, still-births, congenital malformations, learning and other neurodevelopmental disabilities in their village. The response of the Dorset Health Authority (DHA) included the examination of background information from the Ministry of Defence, national data on congenital malformations in Dorset, health information collected by campaigners and a systematic health survey conducted by the DHA among former and current residents of East Lulworth. The investigation did not confirm the presence of a cluster. It is debatable whether the DHA should have proceeded with their survey when none of the other more immediately available results indicated the presence of a cluster.     

A modified likelihood ratio test for homogeneity in finite mixture models

Testing for homogeneity in finite mixture models has been investigated by many researchers. The asymptotic null distribution of the likelihood ratio test (LRT) is very complex and difficult to use in practice. We propose a modified LRT for homogeneity in finite mixture models with a general parametric kernel distribution family. The modified LRT has a χ-type of null limiting distribution and is asymptotically most powerful under local alternatives. Simulations show that it performs better than competing tests. They also reveal that the limiting distribution with some adjustment can satisfactorily approximate the quantiles of the test statistic, even for moderate sample sizes.