A comparison of regularization methods applied to the linear discriminant function with high-dimensional microarray data

Classification of gene expression microarray data is important in the diagnosis of diseases such as cancer, but often the analysis of microarray data presents difficult challenges because the gene expression dimension is typically much larger than the sample size. Consequently, classification methods for microarray data often rely on regularization techniques to stabilize the classifier for improved classification performance. In particular, numerous regularization techniques, such as covariance-matrix regularization, are available, which, in practice, lead to a difficult choice of regularization methods. In this paper, we compare the classification performance of five covariance-matrix regularization methods applied to the linear discriminant function using two simulated high-dimensional data sets and five well-known, high-dimensional microarray data sets. In our simulation study, we found the minimum distance empirical Bayes method reported in Srivastava and Kubokawa [Comparison of discrimination methods for high dimensional data, J. Japan Statist. Soc. 37(1) (2007), pp. 123–134], and the new linear discriminant analysis reported in Thomaz, Kitani, and Gillies [A Maximum Uncertainty LDA-based approach for Limited Sample Size problems – with application to Face Recognition, J. Braz. Comput. Soc. 12(1) (2006), pp. 1–12], to perform consistently well and often outperform three other prominent regularization methods. Finally, we conclude with some recommendations for practitioners.     

Improving bank operations: A case study at BancOhio/Ohio National Bank

The paper describes the procedures employed at Ohio National Bank to improve operations of the check handling and clearing system. It illustrates the approaches utilized to (1) schedule messenger vehicles, (2) determine worker shift schedules, (3) forecast daily work loads and (4) develop work priorities. These four tasks improved productivity and reduced float at the bank. Also discussed is the data required to utilize the formal planning procedures illustrated. The paper indicates the financial impact of this work and future efforts in a dynamic banking environment.     

Violence at work: An issue for the 1990s

Violence and conflict appear to be increasingly common aspects of everyday life, to the point where people take them into consideration when planning their activities and feel anxious about their possible occurrence. It is not only actual violence which offers a contemporary source of stress but also the threat of violence, although subjective estimates of risk are not always accurate. For example, it would appear that while the elderly feel the most threatened, the greatest risk is to those in their late teens and early twenties. This discrepancy between objective and subjective risk is understandable in terms of the different factors which have been shown to drive the subjective assessment of risk: availability of information, controllability and magnitude of outcome. Often it is the media which provides us with the information that we have on violence, and it is that presentation of information which helps shape our assessment of risk. For example, attacks by young persons on the elderly may be more dramatic and newsworthy than, albeit more frequent, attacks on other young persons. Thus they are reported to a greater extent and a distorted impression of risk begins to develop, which may be reinforced by realistic feelings of potential helplessness by the elderly in the face of any such attack, and fear of the magnitude of the consequences of violence. Whatever the real basis for a fear of violence, the available statistics in most European and North American countries suggests that, even taking into account the effects of reporting bias, acts of violence are increasing.     

Call my bluff

Poker used to be the card game of choice for hard men late at night in smoke-filled rooms. Now online poker is bidding for respectability and a site on the home computer. Phil Woodward gives us the straight dope.     

Investigating the link between the Pill and cancer

Does the contraceptive pill increase the risk of cancer? The question has been asked ever since the pill was introduced, and is one that must worry almost every woman in the country. Small wonder that when the results of a long-term study, which began 40 years ago, came out in the autumn it made front-page headlines. As Phil Hannaford explains, answering the question was not straightforward.     

ESTIMATING EQUATIONS AND NON-LINEAR FUNCTIONAL RELATIONSHIPS

A nonlinear functional relationship is defined as an R-dimensional manifold in P-dimensional space. The formulation of the model may be explicitly in terms of R-dimensional vectors of incidental parameters or implicitly by a (P-R)-dimensional vector function of constraints. The objective is to estimate and make inference about a K-vector of parameters θ which defines the manifold. Each observed P-vector has its expectation lying on the manifold, and the error vector has a variance matrix defined in terms of a further vector of parameters The theory of estimating equations in the presence of incidental parameters is extended and applied to the explicit formulation, to give equations suitable for estimating θ given knowledge of only the first two moments. The method has a geometrical interpretation. Estimating equations for are chosen to be those which would be optimal if the normality assumption were true. First order corrections to the biases of these estimates are included. An example where the manifold is a circle centred on the origin is used to illustrate the theory. Further examples incorporate more general features, including the estimation of two variance parameters and estimation in higher dimensions.     

Training for No Secrets : A strategic initiative

Current Department of Health guidance on multi-agency policy and procedure to protect vulnerable adults from abuse requires the design and implementation of comprehensive training programmes. This paper identifies three issues of critical significance to the development of a local training strategy, namely, language ('vulnerability' versus 'rights'), the relative significance of 'awareness', and the scheduling of training in relation to overall policy development. These issues are illustrated by a local training course which, in addition to imparting basic information on the new agenda and locating the latter within the wider context of adult welfare services generally, actively facilitated practitioners' contributions to multi-agency policy development. The outcomes of this initiative are reported in terms of the Department of Health's radical vision of 'mainstreaming' staff involvement.