An Introduction to Multivariate Statistical Analysis

A permutation test is proposed for examining the significance of effects in unreplicated factorial experiments. The procedure tests each effect with a separate sampling distribution using a test statistic that is equivalent to the optimal invariant decision rule of Birnbaum. The proposed test is more flexible than other methods proposed for the same situation because it requires no a priori assumptions regarding the underlying distribution of the data nor does it impose any practical restriction on the number of potentially significant effects present.     

Angewandte Multivariate Statistik

Multivariate quality characteristics are often monitored using a single statistic or a few statistics. However, it is difficult to determine the causes of an out-of-control signal based on a few summary statistics. Therefore, if a control chart for the mean detects a change in the mean, the quality engineer needs to determine which means shifted and the directions of the shifts to facilitate identification of root causes. We propose a Bayesian approach that gives a direct answer to this question. For each mean, an indicator variable that indicates whether the mean shifted upward, shifted downward, or remained unchanged is introduced. Prior distributions for the means and indicators capture prior knowledge about mean shifts and allow for asymmetry in upward and downward shifts. The mode of the posterior distribution of the vector of indicators or the mode of the marginal posterior distribution of each indicator gives the most likely scenario for each mean. Evaluation of the posterior probabilities of all possible values of the indicators is avoided by employing Gibbs sampling. This renders the computational cost more affordable for high-dimensional problems. This article has supplementary materials online.     

Applied Statistical Techniques

This article forecasts the path of statistical computing in the next decade. Its premise is that technology will influence statistical computing more than other factors. This forecast is based on contemporary observations of the field over the last 40 years and on a supposition that extrapolating these trends is not unreasonable. The technology driving this forecast includes not only hardware, but also the software that provides the infrastructure for individual and community interaction with computers. We should not be surprised to see a proliferation of intelligent data analysis systems embedded in everyday objects and Web sites; automated visualizations for data discovery; analytic systems that are accessible by nonstatisticians (a trend toward simplicity and away from comprehensiveness); distributed analytic systems that talk to each other, fuse disparate data in real time, and draw conclusions on the evidence; and communities of open-source developers exceeding the scope and capabilities of commercial companies. Whether computer scientists eventually take over this field will depend on how actively statisticians participate. Statisticians interested in statistical computing and its future incarnations will have to engage in joint research with computer scientists to continue to have an influence.