Hugh A. Chipman, Technometrics Editor
In new problems, sometimes age-old questions emerge unexpectedly. For instance, in trying to learn about a packet communication network, we uncover a question central to optimal design of experiments: how to extract maximal information from a minimal number of samples.
… [I]n trying to learn about a packet communication network, we uncover a question central to optimal design of experiments: how to extract maximal information from a minimal number of samples.
In the paper “Design of Experiments for Categorical Repeated Measurements in Packet Communication Networks,” Ben Parker, Steven Gilmour, and John Schormans develop experimental designs to optimally gather real-time information in the highly constrained environment of packet communication networks. Almost all broadband communication (e.g., the Internet) uses routers to store and forward packet-based data across the network. Queues build within the router’s buffers, and for this reason, the most significant cause of data loss in these networks is the intermittent overflow of these packet buffers.
Direct evaluation of packet loss probability or mean packet delay is typically impossible, due to technical, security, or logistical constraints. Data are instead gathered by sending survey packets, called probes, into the buffer and by recording measurements on the probe packets. This kind of probing has the unwanted consequence of potentially increasing the congestion we seek to measure. A classical design problem emerges: to gather the most information from the probes, while using as few probes as possible. The paper models the buffer as a discrete time Markov chain, optimally designing the observation times for the chain, deriving both exact and continuous optimal designs. For common optimality criteria, measuring at a uniform rate may not be optimal. This has significance for influencing commercial practice, as uniform probing is standard.
Balancing competing objectives to select an optimal experimental design involves flexibly combining measures to select a winner. Moving beyond simple combinations of optimality criteria and heuristic methods, Lu Lu, Christine Anderson-Cook, and Timothy Robinson develop a framework for this search in their paper, “Optimization of Designed Experiments Based on Multiple Criteria Utilizing a Pareto Frontier.” The Pareto approach identifies a suite of potential best designs based on different emphases of the objectives. A new algorithm more efficiently explores candidate designs by populating the Pareto frontier with all possible contending designs identified during the search. Graphical methods enable the user to easily explore design robustness to different weightings of the competing objectives and trade-offs between criteria among competing designs.
For many expensive deterministic computer simulators, outputs are observed without error, and the desired statistical emulator is an interpolator. The commonly used Gaussian spatial process model can be computationally unstable, especially when design points are very close together in the input space. Pritam Ranjan, Ronald Haynes, and Richard Karsten improve on the popular solution of introducing a small nugget (or jitter) parameter in the model. In “A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data,” they propose a lower bound on the nugget that minimizes over-smoothing and an iterative regularization approach to construct a predictor that further improves the interpolation accuracy.
The analysis of data streams requires methods that can cope with a very high volume of data points. Gordon Ross, Dimitris Tasoulis, and Niall Adams, in the paper “Nonparametric Monitoring of Data Streams for Changes in Location and Scale,” develop a nonparametric framework for detecting changes in data streams with challenging requirements: robust estimation, constant computational complexity, and fixed memory. Changes in both location and scale are detectable, and the false alarm rate can be controlled even when the data distribution is unknown.
On a related theme, the paper “On Nonparametric Statistical Process Control of Univariate Processes,” by Peihua Qiu and Zhonghua Li, considers statistical process control of univariate processes when the parametric form of the process distribution is unavailable. By converting the data to categorical form, conventional assumptions on the process distribution are relaxed, yielding control charts that are surprisingly robust and efficient.
In “Sparse Discriminant Analysis,” Line Clemmensen, Trevor Hastie, Daniela Witten, and Bjarne Ersbøll consider the problem of performing interpretable high-dimensional classification with many features and few observations. Their sparse discriminant analysis method simultaneously performs classification and feature selection. By basing the method on the optimal scoring interpretation of linear discriminant analysis, extensions to mixtures of Gaussians enable nonlinear classification a subgroup interpretation. The method also provides low-dimensional views of the discriminative directions.
In the paper “Comparing Spatial Predictions,” Amanda Hering and Marc Genton develop a hypothesis test to determine whether a significant difference in the spatial predictions produced by two competing models exists on average across the entire spatial domain of interest. The approach extends earlier work on comparing time series forecasts, incorporating unique features of spatial data. Making minimal assumptions, the test allows for non-Gaussian distributions and spatial correlation. An example based on daily average wind speeds in Oklahoma is used for illustration.
In “Two-Way MANOVA with Unequal Cell Sizes and Unequal Cell Covariance Matrices,” Jin-Ting Zhang develops an approximate Hotelling T2 test for heteroscedastic two-way MANOVA. An extension of the test for heteroscedastic multi-way MANOVA is briefly described. Simulations demonstrate superior performance in terms of size and power, and a data set from a smoking cessation trial is analyzed to illustrate the methodologies.
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