Paper: arXiv 2605.12547

Authors: Kyriakos Christodoulides

Abstract

Public procurement is vulnerable to error, fraud and corruption, yet high transaction volumes overwhelm oversight. While research often focuses on tender-stage anomalies, post-award payments remain underexplored. Since labelled datasets are rare and existing methods such as Benford’s Law face restrictive assumptions, there is a need for additional interpretable, unsupervised frameworks that augment oversight and simplify management. This paper introduces the Structural Heterogeneity Index (SHI), a composite statistic for one-dimensional samples defined by four components: modality, asymmetry, tail behaviour, and structural dispersion. The Payment Heterogeneity Index (PHI) is its multiplicative instance for post-award payments. PHI combines a tail-behaviour component, sensitive to outliers and point clustering, with a structural-dispersion component summarising payment regime architecture. Structural dispersion is computed via Gaussian Mixture Model (GMM) estimation, integrating within-regime variability, prevalence, and separation from the dominant mode. Applied to UK municipal procurement data, PHI isolates a financially significant cohort (10.1% of high-volume suppliers) whose structural signatures deviate from the population and interact with recurring payment anchors. Permutation and Kolmogorov-Smirnov tests confirm that high-PHI suppliers exhibit statistically significant structural differences. A forensic review by a Certified Fraud Examiner supports the plausibility of the prioritised cases. Comparison shows PHI uniquely identifies regime separation obscured by metrics like the Coefficient of Variation (\r{ho}=0.310). PHI functions as an effective discovery tool where no confirmed labels exist, offering a transparent, lightweight screening mechanism for post-award oversight.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper combines formal Gaussian Mixture Model (GMM) estimation and composite statistical index construction with a practical, data-heavy application on real-world municipal procurement datasets. It bridges theoretical structural analysis with actionable, audit-ready triage workflows, demonstrating both analytical depth and functional utility.

Research Flowchart

  flowchart TD
    A[<b>Research Goal:</b> Unsupervised oversight for high-volume procurement post-award payments] --> B[<b>Data Input:</b> UK Municipal Procurement Transactions]
    B --> C[<b>Computational Framework:</b> Calculate Structural Heterogeneity Index (SHI/PHI) using GMMs]
    C --> D[<b>Methodology:</b> Combine Tail-behavior & Structural Dispersion components]
    D --> E[<b>Validation:</b> Statistical Significance Tests & Forensic Expert Review]
    E --> F[<b>Outcomes:</b> Identified high-risk supplier cohort & effective lightweight discovery tool]

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0 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.