Report of the Editors—1995Atkinson, A. C.; Young, G. A.
doi: 10.1111/j.2517-6161.1996.tb02064.xpmid: N/A
We have two Joint Editors and a panel of around 16 Associate Editors, each of whom customarily serves for four years so, as usual, there have been several changes in the editorial arrangements over the last year. Anthony Atkinson retires as Joint Editor at the end of December 1995 and will be replaced by Chris Jones (The Open University). The new Associate Editors are Ray Chambers (University of Southampton), John Copas (University of Warwick), David Draper (University of Bath) and David Madigan (University of Washington). In addition Trevor Sweeting has agreed to continue beyond his original four‐year term. The retiring Associate Editors are John Haslett, Tony Lawrance, Roger Sugden and Luke Tierney. We take this opportunity to thank them and all the Associate Editors for their hard work for the journal.
Inferences from Multinomial Data: Learning About a Bag of MarblesWalley, Peter
doi: 10.1111/j.2517-6161.1996.tb02065.xpmid: N/A
A new method is proposed for making inferences from multinomial data in cases where there is no prior information. A paradigm is the problem of predicting the colour of the next marble to be drawn from a bag whose contents are (initially) completely unknown. In such problems we may be unable to formulate a sample space because we do not know what outcomes are possible. This suggests an invariance principle: inferences based on observations should not depend on the sample space in which the observations and future events of interest are represented. Objective Bayesian methods do not satisfy this principle. This paper describes a statistical model, called the imprecise Dirichlet model, for drawing coherent inferences from multinomial data. Inferences are expressed in terms of posterior upper and lower probabilities. The probabilities are initially vacuous, reflecting prior ignorance, but they become more precise as the number of observations increases. This model does satisfy the invariance principle. Two sets of data are analysed in detail. In the first example one red marble is observed in six drawings from a bag. Inferences from the imprecise Dirichlet model are compared with objective Bayesian and frequentist inferences. The second example is an analysis of data from medical trials which compared two treatments for cardiorespiratory failure in newborn babies. There are two problems: to draw conclusions about which treatment is more effective and to decide when the randomized trials should be terminated. This example shows how the imprecise Dirichlet model can be used to analyse data in the form of a contingency table.
The Usefulness of Optimum Experimental DesignsAtkinson, A. C.
doi: 10.1111/j.2517-6161.1996.tb02067.xpmid: N/A
Optimum experimental designs were originally developed by Kiefer, mainly for response surface models. This survey of recent developments emphasizes potential or actual usefulness. For linear models the construction of exact designs, particularly over irregular design regions, is stressed, as is the blocking of response surface designs. Other important areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions: several industrial examples are mentioned. Both D‐ and c‐optimum designs are found for a non‐linear model of the economic response of cereal production to fertilizer level, the c‐optimum design being for the conditions of maximum economic return. Locally optimum and Bayesian designs are both described. Similar results for generalized linear models lead to designs for the LD95 in a logistic model in which male and female subjects respond differently. Designs with structure in the variance suggest alternatives to the potentially wasteful product designs of Taguchi. Designs for sequential clinical trials to include random balance are presented. The last section outlines some applications, including life testing and models in which time is a factor.
Experimental Design and Observation for Large SystemsBates, R. A.; Buck, R. J.; Riccomagno, E.; Wynn, H. P.
doi: 10.1111/j.2517-6161.1996.tb02068.xpmid: N/A
Large systems require new methods of experimental designs suitable for the highly adaptive models which are employed to cope with complex non‐linear responses and high dimensionality of input spaces. The area of computer experiments has started to provide such designs especially Latin hypercube and lattice designs. System decomposition, prevalent in several branches of engineering, can be employed to decrease complexity. A combination of system decomposition using a sparse matrix method, experimental design and modelling is applied to one example of an electrical circuit simulator producing a usable emulator of the circuit for use in optimization and sensitivity analysis.
Estimation of Population Exposure in Ecological StudiesPlummer, Martyn; Clayton, David
doi: 10.1111/j.2517-6161.1996.tb02070.xpmid: N/A
This paper discusses design issues in 'ecological studies' —epidemiological studies in which the relationship between disease and behavioural and environmental determinants is studied at the population rather than the individual level. The number of study populations has little relevance beyond a certain point, the power and precision being limited by the total number of disease events and by the size of the sample surveys used to estimate the distributions of determinants within populations. In most circumstances, optimal design requires the size of the sample surveys in each population to be related to the number of disease events which will occur in it, and for sampling to be stratified by age and/or sex.
Reducing the Use of Laboratory Animals in Toxicological Research and Testing by Better Experimental DesignFesting, Michael F. W.; Lovell, David P.
doi: 10.1111/j.2517-6161.1996.tb02071.xpmid: N/A
More than 50 million animals are used in biomedical research in the world each year. It is highly desirable that this number is reduced both for ethical and for economic reasons. Better experimental design could lead to the use of fewer animals and improve the repeatability of animal experiments so that alternative methods would be easier to validate. Screening experiments aimed at identifying rodent carcinogens would be more powerful if more than one strain of mice and/or rats were used. Attempts to validate alternative test methods by using chemicals already tested in the Draize test for eye irritation are complicated by limited information on the interexperiment variability of the whole animal test. In academic toxicological research, surveys suggest that many experiments are poorly designed, and some seem to be unnecessarily large.
Discriminant Analysis by Gaussian MixturesHastie, Trevor; Tibshirani, Robert
doi: 10.1111/j.2517-6161.1996.tb02073.xpmid: N/A
Fisher‐Rao linear discriminant analysis (LDA) is a valuable tool for multigroup classification. LDA is equivalent to maximum likelihood classification assuming Gaussian distributions for each class. In this paper, we fit Gaussian mixtures to each class to facilitate effective classification in non‐normal settings, especially when the classes are clustered. Low dimensional views are an important by‐product of LDA—our new techniques inherit this feature. We can control the within‐class spread of the subclass centres relative to the between‐class spread. Our technique for fitting these models permits a natural blend with nonparametric versions of LDA.