The Payment Heterogeneity Index: An Integrated Unsupervised Framework for High-Volume Procurement Oversight and Decision Support

TL;DR

This paper introduces the Payment Heterogeneity Index (PHI), an unsupervised, interpretable framework for high-volume procurement payment oversight, capable of identifying anomalous payment patterns and regimes in large datasets.

Contribution

It develops a novel composite statistic, PHI, combining GMM parameters and non-parametric statistics for transparent, lightweight procurement anomaly detection.

Findings

PHI identifies a significant cohort with distinct payment patterns.

Statistical tests support the structural differences detected by PHI.

PHI reveals regime separation not visible through traditional metrics.

Abstract

Public procurement is vulnerable to error, fraud, and corruption, particularly as high transaction volumes overwhelm oversight. While research often focuses on tender-stage anomalies, post-award payment monitoring remains underexplored. Since labelled datasets are rare and methods like Benford's Law face restrictive assumptions, there is a need for interpretable, unsupervised frameworks for high-volume procurement oversight and decision support. This paper introduces the Structural Heterogeneity Index (SHI), a composite statistic for one-dimensional samples, and its payment-specific instantiation, the Payment Heterogeneity Index (PHI), characterising payment structure and latent regimes. It incorporates Gaussian Mixture Model (GMM) parameters alongside non-parametric statistics, integrating four interpretable components: modality, asymmetry, tail behaviour, and structural dispersion. Uniquely, the tail-behaviour component captures both distributional heaviness and extreme-value concentration, while structural-dispersion combines the variability, prevalence, and separation of latent payment regimes. Applied to UK municipal procurement data, PHI identifies a financially significant cohort (0.6\% of suppliers; 10.1\% of high-volume vendors) with structurally distinct payment patterns. Statistical testing further supports these differences, and targeted human verification confirms the plausibility of prioritised cases. Comparative analysis shows PHI reveals regime separation obscured by the Coefficient of Variation ($\rho = 0.310$). PHI provides a transparent, decomposable, and computationally lightweight framework for procurement integrity oversight and targeted audit prioritisation.