Modelling and detecting mild and gross anomalies in circular data via double-contaminated models

2026-06-28

AI Summary

This study addresses the challenge of distinguishing between mild and severe outliers in circular data by proposing a three-component Bayesian mixture model. The model employs a symmetric unimodal circular distribution—such as the von Mises or wrapped normal—as a reference component, incorporates a uniform distribution to capture severe outliers, and introduces a low-concentration component sharing the same mean to represent mild anomalies. This dual-contamination framework uniquely enables automatic identification and quantification of both outlier types within a unified probabilistic structure, without requiring predefined thresholds. It further yields interpretable estimates of outlier proportions and dispersion inflation. Simulation studies and real-data analyses—including applications to animal movement and wind direction—demonstrate that the proposed approach substantially enhances model robustness and effectively uncovers latent structures in directional data.

Abstract

In this paper, we propose a model-based framework to robustify inference for circular data in the presence of anomalous observations, distinguishing between mild and gross anomalies. Starting from a unimodal and symmetric reference model on $[0,2π)$, parametrized by a mean direction and concentration, we construct a family of finite mixtures: a gross-anomaly model obtained by adding a circular uniform component; a mild-anomaly (contaminated) model obtained by mixing the reference distribution with a less concentrated version sharing the same mean direction; and a general three-component specification combining both models, the double-contaminated model. Posterior component probabilities provide an automatic classification of observations without ad hoc thresholds, while the mixing weights yield interpretable measures of anomaly prevalence and dispersion inflation. For illustration, we consider two classical circular reference distributions, the wrapped normal and von Mises. The methodology is evaluated through an extensive simulation study and three real-data applications involving animal movement directions and wind directions. The results indicate that jointly modelling mild and gross departures improves model fit and yields an informative decomposition of the directional data, demonstrating that mixture-based robustness is valuable not only for anomaly detection but also for the interpretation and the identification of latent structure in directional data.

Problem

• circular data
• anomaly detection
• mild anomalies
• gross anomalies
• robust inference

Innovation

• double-contaminated model
• circular data
• robust inference
• anomaly detection
• mixture modeling