arXiv subjects

Jonathan W. Stallrich

Publications and source records attributed to Jonathan W. Stallrich.

5 recordsLinked to original sources

arXiv2026

Revisiting Penalized Likelihood Estimation for Deterministic Computer Experiments

Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it can be plagued by numerical issues in small data settings. The addition of a nugget may help but is not a cure-all. Penalized likelihood methods may improve upon traditional MLE, but their success depends on tuning parameter selection. We introduce a new cross-validation (CV) metric called ``decorrelated prediction error'' (DPE), within the penalized likelihood framework for GPs. Inspired by the Mahalanobis distance, DPE provides more consistent and reliable tuning parameter selection than traditional metrics like prediction error, particularly for $K$-fold CV. Our proposed metric performs comparably to standard MLE when penalization is unnecessary and outperforms traditional tuning parameter selection metrics in scenarios where regularization is beneficial, especially under the one-standard error rule.

stat.ME↗

arXiv2025

Powerful Foldover Designs

The foldover technique for screening designs is well known to guarantee zero aliasing of the main effect estimators with respect to two factor interactions and quadratic effects. It is a key feature of many popular response surface designs, including central composite designs, definitive screening designs, and most orthogonal, minimally-aliased response surface designs. In this paper, we show the foldover technique is even more powerful, because it produces degrees of freedom for a variance estimator that is independent of model selection. These degrees of freedom are characterized as either pure error or fake factor degrees of freedom. A fast design construction algorithm is presented that minimizes the expected confidence interval criterion to maximize the power of screening main effects. An augmented design and analysis method is also presented to avoid having too many degrees of freedom for estimating variance and to improve model selection performance for second order models. Simulation studies show our new designs are at least as good as traditional designs when effect sparsity and hierarchy hold, but do significantly better when these effect principles do not hold. A real data example is given for a 20-run experiment where optimization of ethylene concentration is performed by manipulating eight process parameters.

stat.ME↗

arXiv2025

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↗

arXiv2024

Optimal Designs for Two-Stage Inference

The analysis of screening experiments is often done in two stages, starting with factor selection via an analysis under a main effects model. The success of this first stage is influenced by three components: (1) main effect estimators' variances and (2) bias, and (3) the estimate of the noise variance. Component (3) has only recently been given attention with design techniques that ensure an unbiased estimate of the noise variance. In this paper, we propose a design criterion based on expected confidence intervals of the first stage analysis that balances all three components. To address model misspecification, we propose a computationally-efficient all-subsets analysis and a corresponding constrained design criterion based on lack-of-fit. Scenarios found in existing design literature are revisited with our criteria and new designs are provided that improve upon existing methods.

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↗