Applied Statistics Algorithms

This article describes a family of Resolution IIIdesigns for which the usual advice regarding foldover—reversing all factors—is ill advised. The smallest such designs have 16 runs. For designs in this family, alternative foldover fractions not only increase the resolution to IV, but also separate some of the aliased two-factor interactions. Although Resolution IV designs obtained by reversing all factors provide fewer than half the degrees of freedom for estimating two-factor interactions, the recommended foldovers for designs in this class permit estimation of many more two-factor interactions. This result implies that designs in this class make attractive initial designs, even if they are not minimum aberration.     

Applied Statistics: Analysis of Variance and Regression

A new robust criterion for experimental designs is proposed. For a given design, the criterion is to minimize, over all possible run orders, the absolute value of the change of the variance function due to possible correlation between the observations. The resulting design is robust against possible auto-correlation among the observations in the sense that confidence-interval coverage levels are maintained accurately. Applications are given for 2^k factorial designs and one mixed-level fractional experiment, and robust runs are obtained. Computational strategies are also discussed, and a simulated annealing algorithm is developed to search for robust designs.     

Applied Statistics: A First Course in Inference

An important task of the U.S. Nuclear Regulatory Commission is to examine annual operating data from the nation's population of nuclear power plants for trends over time. We are interested here in trends in the scram rate at 66 commercial nuclear power plants based on annual observed scram data from 1984–1993. For an assumed Poisson distribution on the number of unplanned scrams, a gamma prior, and an appropriate hyperprior, a parametric empirical Bayes (PEB) approximation to a full hierarchical Bayes formulation is used to estimate the scram rate for each plant for each year. The PEB-estimated prior and posterior distributions are then subsequently smoothed over time using an exponentially weighted moving average. The results indicate that such bidirectional shrinkage is quite useful for identifying reliability trends over time.     

Neural Networks in Applied Statistics

Artificial neural networks are computer algorithms or computer programs derived in part from attempts to model the activity of nerve cells. They have been applied to pattern recognition, classification, and optimization problems in the physical and chemical sciences, as well as in other fields. We introduce the principles of the multilayer feedforward network that is among the most commonly used neural networks in practical problems. The relevance of neural network models for the applied statistician is considered using a time series prediction problem as an example. The multilayer feedforward neural network uses a nonlinear function of the predictors to obtain predictions for future time series values. We illustrate the considerations involved in specifying a neural network model and evaluate the accuracy of neural network models relative to the accuracy obtained using other computer-intensive, nonmodel-based techniques.