Scholarlink

<p>Comparative judgement studies elicit quality assessments of objects through pairwise comparisons, typically analysed using the Bradley–Terry model. A challenge in these studies is experimental design, specifically, determining the optimal pairs to compare to maximize statistical efficiency. Constructing static experimental designs for these studies requires spectral decomposition of a covariance matrix over pairs of pairs, which becomes computationally infeasible for studies with a large number of objects. We propose a scalable method based on reduced basis decomposition that bypasses explicit construction of this matrix, achieving computational savings of two to three orders of magnitude. We establish eigenvalue bounds guaranteeing approximation quality and characterise the rank structure of the design matrix. Simulations demonstrate speedup factors exceeding 100 for studies with 64 or more objects, with negligible approximation error. We apply the method to construct designs for a 452-region spatial study in under 7&#xa0;min, which was not previously possible, and enable real-time design updates for classroom peer assessment, reducing computation time from 15&#xa0;min to 15&#xa0;s.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A reduced basis decomposition approach to efficient data collection in pairwise comparison studies

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月21日

查看全文
  • Jiahua Jiang,
  • Joseph Marsh,
  • Rowland Seymour

摘要

Comparative judgement studies elicit quality assessments of objects through pairwise comparisons, typically analysed using the Bradley–Terry model. A challenge in these studies is experimental design, specifically, determining the optimal pairs to compare to maximize statistical efficiency. Constructing static experimental designs for these studies requires spectral decomposition of a covariance matrix over pairs of pairs, which becomes computationally infeasible for studies with a large number of objects. We propose a scalable method based on reduced basis decomposition that bypasses explicit construction of this matrix, achieving computational savings of two to three orders of magnitude. We establish eigenvalue bounds guaranteeing approximation quality and characterise the rank structure of the design matrix. Simulations demonstrate speedup factors exceeding 100 for studies with 64 or more objects, with negligible approximation error. We apply the method to construct designs for a 452-region spatial study in under 7 min, which was not previously possible, and enable real-time design updates for classroom peer assessment, reducing computation time from 15 min to 15 s.