Optimal Supersaturated Designs for Lasso Sign Recovery

Supersaturated designs, in which the number of factors exceeds the number of runs, are often constructed under a heuristic criterion that measures a design's proximity to an unattainable orthogonal design. Such a criterion does not directly measure a design's quality in terms of screening. To address this disconnect, we develop optimality criteria to maximize the lasso's sign recovery probability. The criteria have varying amounts of prior knowledge about the model's parameters. We show that an orthogonal design is an ideal structure when the signs of the active factors are unknown. When the signs are assumed known, we show that a design whose columns exhibit small, positive correlations are ideal. Such designs are sought after by the Var(s+)-criterion. These conclusions are based on a continuous optimization framework, which rigorously justifies the use of established heuristic criteria. From this justification, we propose a computationally-efficient design search algorithm that filters through optimal designs under different heuristic criteria to select the one that maximizes the sign recovery probability under the lasso

Approximate Model Spaces for Model-Robust Experiment Design *

Abstract Optimal designs depend upon a prespecified model form. A popular and effective modelrobust alternative is to design with respect to a set of models instead of just one. However, model spaces associated with experiments of interest are often prohibitively large and so algorithmically-generated designs are infeasible. Here, we present a simple method which largely eliminates this problem by choosing a small set of models which approximates the full set and finding designs that are explicitly robust for this small set. We build our procedure on a restricted columnwise-pairwise algorithm, and explore its effectiveness for two model spaces in the literature. For smaller full model spaces, we find that the designs constructed with the new method compare favorably to robust designs which utilize the full model space, with construction times smaller by orders of magnitude. We also construct designs that heretofore have been unobtainable due to the size of their model spaces. Supplementary material (available online) includes code, designs, and additional results

Approximate Model Spaces for Model-Robust Experiment Design

<p>Optimal designs depend upon a prespecified model form. A popular and effective model-robust alternative is to design with respect to a set of models instead of just one. However, model spaces associated with experiments of interest are often prohibitively large and so algorithmically generated designs are infeasible. Here, we present a simple method that largely eliminates this problem by choosing a small set of models that approximates the full set and finding designs that are explicitly robust for this small set. We build our procedure on a restricted columnwise-pairwise algorithm, and explore its effectiveness for two model spaces in the literature. For smaller full model spaces, we find that the designs constructed with the new method compare favorably with robust designs that use the full model space, with construction times reduced by orders of magnitude. We also construct designs that heretofore have been unobtainable due to the size of their model spaces. Supplementary material (available online) includes code, designs, and additional results.</p

Beyond Normal: Preparing Undergraduates for the Work Force in a Statistical Consulting Capstone

<p>In this article we chronicle the development of the undergraduate statistical consulting course at Miami University, from canned to client-based projects, and argue that if the course is well designed with suitable mentoring, students can perform remarkably sophisticated analyses of real-world data problems that require solutions beyond the methods encountered in previous classes. We review the historical context in which the consulting class evolved, describe the logistics of implementing it, and review assessment and student reaction to the course. We also illustrate the types of challenging projects the students are confronted with via two case studies and relate the skills learned and reinforced in this consulting class model to the skills demanded in the modern statistical work force. This course also provides an opportunity to strengthen and nurture key points from the new American Statistical Association guidelines for undergraduate programs: namely, communicating analyses of real and complex data that require the application of diverse statistical models and approaches. Supplementary materials for this article are available online.</p> <p>[Received December 2014. Revised July 2015.]</p