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

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.…
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