arXiv subjects

Alan R. Vazquez

Publications and source records attributed to Alan R. Vazquez.

5 recordsLinked to original sources

arXiv2026

Prompt engineering using order-of-addition experiments: An application to generating two-level fractional factorial designs

Large language models (LLMs) are becoming ubiquitous in engineering and science because they can turn prompts into data analysis code, experimental designs, formulations of optimization problems, among other applications. However, many LLMs suffer from a phenomenon called order dependency, in which the order of phrases in the prompt affects their performance on a given task. To overcome this issue, we introduce a systematic method that uses order-of-addition experiments to quantify the ordering effect of elements in a prompt and identify their best positions. We demonstrate our methodology by constructing two-level fractional factorial designs using state-of-the-art LLMs. We show that order-of-addition experiments can elucidate order dependency in these LLMs, and can help us to identify a high-quality prompt configuration for the task.

stat.AP↗

arXiv2026

A systematic assessment of Large Language Models for constructing two-level fractional factorial designs

Two-level fractional factorial designs permit the study multiple factors using a limited number of runs. Traditionally, these designs are obtained from catalogs available in standard textbooks or statistical software. However, modern Large Language Models (LLMs) can now produce two-level fractional factorial designs, but the quality of these designs has not been previously assessed. In this paper, we perform a systematic evaluation of two popular classes of LLMs, namely GPT and Gemini models, to construct two-level fractional factorial designs with 8, 16, and 32 runs, and 4 to 26 factors. To this end, we use prompting techniques to develop a high-quality set of design construction tasks for the LLMs. We compare the designs obtained by the LLMs with the best-known designs in terms of resolution and minimum aberration criteria. We show that the LLMs can effectively construct optimal 8-, 16-, and 32-run designs with up to eight factors.

stat.ME↗

arXiv2025

Constructing Large Orthogonal Minimally Aliased Response Surface Designs by Concatenating Two Definitive Screening Designs

Orthogonal minimally aliased response surface (OMARS) designs permit the study of quantitative factors at three levels using an economical number of runs. In these designs, the linear effects of the factors are neither aliased with each other nor with the quadratic effects and the two-factor interactions. Complete catalogs of OMARS designs with up to five factors have been obtained using an enumeration algorithm. However, the algorithm is computationally demanding for designs with many factors and runs. To overcome this issue, we propose a construction method for large OMARS designs that concatenates two definitive screening designs and improves the statistical features of its parent designs. The concatenation employs an algorithm that minimizes the aliasing among the second-order effects using foldover techniques and column permutations for one of the parent designs. We study the properties of the new OMARS designs and compare them with alternative designs in the literature.

stat.ME↗

arXiv2024

A review of Design of Experiments courses offered to undergraduate students at American universities

Design of Experiments (DoE) is a relevant class to undergraduate students in the sciences, because it teaches them how to plan, conduct, and analyze experiments. In the literature on DoE, there are several contributions to its pedagogy, such as easy-to-use class experiments, virtual experiments, and software to construct experimental designs. However, there are virtually no systematic evaluations of the actual DoE pedagogy. To address this issue, we build the first database of DoE courses offered to undergraduate students in the United States. The database has records on courses offered from 2019 to 2022 at the best universities in the US News Best National Universities ranking of 2022. Specifically, it has data on 18 general and content-specific features of 206 courses. To study the DoE pedagogy, we analyze the database using descriptive statistics and text mining. Based on our analysis, we provide instructors with recommendations and teaching material to enhance their DoE courses. The database and material are included in the supplement of this article.

stat.OT↗

arXiv2024

Mathematical programming tools for randomization purposes in small two-arm clinical trials: A case study with real data

Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods use mathematical programming to construct attractive clinical trials that balance the group features, such as their sizes and covariate distributions of their subjects. We review some of these methods and compare their performance with common covariate-adaptive randomization methods for small clinical trials. We introduce an energy distance measure that compares the discrepancy between the two groups using the joint distribution of the subjects' covariates. This metric is more appealing than evaluating the discrepancy between the groups using their marginal covariate distributions. Using numerical experiments, we demonstrate the advantages of the mathematical programming methods under the new measure. In the supplementary material, we provide R codes to reproduce our study results and facilitate comparisons of different randomization procedures.

stat.ME↗