arXiv subjects

David J. Edwards

Publications and source records attributed to David J. Edwards.

6 recordsLinked to original sources

arXiv2025

The use of cross validation in the analysis of designed experiments

Cross-validation (CV) is a common method to tune machine learning methods and can be used for model selection in regression as well. Because of the structured nature of small, traditional experimental designs, the literature has warned against using CV in their analysis. The striking increase in the use of machine learning, and thus CV, in the analysis of experimental designs, has led us to empirically study the effectiveness of CV compared to other methods of selecting models in designed experiments, including the little bootstrap. We consider both response surface settings where prediction is of primary interest, as well as screening where factor selection is most important. Overall, we provide evidence that the use of leave-one-out cross-validation (LOOCV) in the analysis of small, structured is often useful. More general $k$-fold CV may also be competitive but its performance is uneven.

stat.AP↗

arXiv2024

Large Row-Constrained Supersaturated Designs for High-throughput Screening

High-throughput screening, in which multiwell plates are used to test large numbers of compounds against specific targets, is widely used across many areas of the biological sciences and most prominently in drug discovery. We propose a statistically principled approach to these screening experiments, using the machinery of supersaturated designs and the Lasso. To accommodate limitations on the number of biological entities that can be applied to a single microplate well, we present a new class of row-constrained supersaturated designs. We develop a computational procedure to construct these designs, provide some initial lower bounds on the average squared off-diagonal values of their main-effects information matrix, and study the impact of the constraint on design quality. We also show via simulation that the proposed constrained row screening method is statistically superior to existing methods and demonstrate the use of the new methodology on a real drug-discovery system.

stat.ME↗

arXiv2023

A Graphical Comparison of Screening Designs using Support Recovery Probabilities

A screening experiment attempts to identify a subset of important effects using a relatively small number of experimental runs. Given the limited run size and a large number of possible effects, penalized regression is a popular tool used to analyze screening designs. In particular, an automated implementation of the Gauss-Dantzig selector has been widely recommended to compare screening design construction methods. Here, we illustrate potential reproducibility issues that arise when comparing screening designs via simulation, and recommend a graphical method, based on screening probabilities, which compares designs by evaluating them along the penalized regression solution path. This method can be implemented using simulation, or, in the case of lasso, by using exact local lasso sign recovery probabilities. Our approach circumvents the need to specify tuning parameters associated with regularization methods, leading to more reliable design comparisons. This article contains supplementary materials including code to implement the proposed methods.

stat.ME↗

arXiv2023

An Optimal Design Framework for Lasso Sign Recovery

Supersaturated designs investigate more factors than there are runs, and are often constructed under a criterion measuring a design's proximity to an unattainable orthogonal design. The most popular analysis identifies active factors by inspecting the solution path of a penalized estimator, such as the lasso. Recent criteria encouraging positive correlations between factors have been shown to produce designs with more definitive solution paths so long as the active factors have positive effects. Two open problems affecting the understanding and practicality of supersaturated designs are: (1) do optimal designs under existing criteria maximize support recovery probability across an estimator's solution path, and (2) why do designs with positively correlated columns produce more definitive solution paths when the active factors have positive sign effects? To answer these questions, we develop criteria maximizing the lasso's sign recovery probability. We prove that an orthogonal design is an ideal structure when the signs of the active factors are unknown, and a design constant small, positive correlations is ideal when the signs are assumed known. A computationally-efficient design search algorithm is proposed that first filters through optimal designs under new heuristic criteria to select the one that maximizes the lasso sign recovery probability.

math.ST↗

arXiv2019

Monotonic Nonparametric Dose Response Model

Toxicologists are often concerned with determining the dosage to which an individual can be exposed with an acceptable risk of adverse effect. These types of studies have been conducted widely in the past, and many novel approaches have been developed. Parametric techniques utilizing ANOVA and nonlinear regression models are well represented in the literature. The biggest drawback of parametric approaches is the need to specify the correct model. Recently, there has been an interest in nonparametric approaches to tolerable dosage estimation. In this work, we focus on the monotonically decreasing dose response model where the response is a percent to control. This poses two constraints to the nonparametric approach. The doseresponse function must be one at control (dose = 0), and the function must always be positive. Here we propose a Bayesian solution to this problem using a novel class of nonparametric models. A basis function developed in this research is the Alamri Monotonic spline (AM-spline). Our approach is illustrated using both simulated data and an experimental dataset from pesticide related research at the US Environmental Protection Agency.

stat.AP↗

arXiv2008

Investigation of Vertical Spiral Resonators for Low Frequency Metamaterial Design

This paper thoroughly explores the characteristics of vertical spiral resonators (VSR). They exhibit rela-tively high Q factors and sizes around a few percent of the free space wavelength, which make them ideal candi-dates for assembling metamaterial devices. A quasistatic model of VSR is obtained from simple analytical ex-pressions, and the effects of certain geometrical parameters on the resonant frequency are investigated.

physics.optics↗