🤖 AI Summary
This study addresses the lack of effective unsupervised monitoring tools for detecting anomalous behaviors in high-volume government procurement payments. The authors propose a Payment Heterogeneity Index (PHI) that integrates four dimensions—modality, asymmetry, tail behavior, and structural dispersion derived from a Gaussian Mixture Model (GMM)—thereby combining tail analysis with structural heterogeneity for the first time to uncover payment mechanism bifurcations overlooked by conventional metrics. Applied to municipal procurement data in the UK, PHI flagged 10.1% of suppliers as anomalous, exhibiting payment patterns markedly divergent from the norm; expert validation confirmed these cases warrant high investigative priority. Notably, PHI demonstrates distinct anomaly detection capability, showing low correlation with the coefficient of variation (ρ = 0.310).
📝 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.