von mises association

This paper addresses regression tasks involving circular-valued outputs (e.g., angles, phases) by proposing a Bayesian nonparametric model based on the von Mises distribution. Unlike conventional approaches—such as wrapped Gaussian processes or radial marginalization—the method constructs a “von Mises pseudo-process” that directly models the input–output mapping on the unit circle, inheriting both maximum-entropy density properties and interpretability. Methodologically, it introduces Stratonovich-style data augmentation to enable efficient Gibbs sampling and devises a novel dual Metropolis–Hastings algorithm for Bayesian inference on circular domains. Evaluated on wind direction forecasting and gait cycle phase estimation, the model achieves state-of-the-art predictive accuracy, superior calibration, and reliable uncertainty quantification—outperforming existing circular regression methods across all metrics.

This work addresses the challenge of uncertainty quantification in direction-of-arrival (DOA) estimation for automotive radar in dense target scenarios. It introduces, for the first time, the von Mises distribution from circular statistics into radar DOA modeling and proposes an ensemble method (ENS) based on this distribution. The ENS outputs uncertainty parameters (μ, κ) that respect directional geometric consistency and enable closed-form likelihood computation, allowing seamless integration into downstream data association modules. Compared to evidential deep learning (EDL), ENS yields lower uncertainty under in-distribution conditions and exhibits greater sensitivity to severe perturbations, whereas EDL demonstrates smoother uncertainty transitions and slightly better ranking consistency, revealing a fundamental trade-off between geometric fidelity and statistical generality in uncertainty modeling.

Angle data regression requires modeling the inherent circular/spherical manifold structure, yet distributional wrapping under noisy observations couples the latent distribution with the wrapping mechanism, hindering tractable inference. This paper proposes the Monotonic Wrapping Gaussian Process (MW-GP), the first approach to decouple these components by introducing a monotonicity assumption on the wrapping function. MW-GP estimates wrapping locations piecewise in the input space and enables robust Bayesian inference via a Student’s *t* likelihood coupled with elliptical slice sampling. The method significantly improves stability and accuracy in modeling angular responses under noise. In synthetic experiments, it outperforms existing wrapping GP methods. Furthermore, it is successfully applied to phase–distance localization of RFID tags, accurately capturing the unidirectional wrapping relationship between frequency and phase angle.

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.

This study addresses the detectability of latent phase-coherent structures in observations on the unit circle, distinguishing between uniform and non-uniform distributions with planted signals. A hypothesis testing framework is developed for circular data, employing hard clustering of arcs under a “flat” null model and von Mises mixture models under a “community” alternative. The work establishes nearly tight information-theoretic detection thresholds for four distinct planted signal models, accommodating unknown location parameters and varying correlation structures. By integrating hypothesis testing, information-theoretic lower bounds, concentration inequalities, and circular statistical modeling, the authors derive matching necessary and sufficient conditions for detection—up to constant factors (and logarithmic terms in some cases)—thereby fully characterizing the detection phase transition boundary across all models.

This study addresses circular response data exhibiting directional structure and within-cluster dependence, as commonly encountered in repeated orientation experiments and movement ecology. The authors propose a mixed-effects model within the generalized angular regression framework, defining the mean direction via a two-dimensional consensus vector and incorporating both a von Mises-distributed circular random intercept and a Gaussian scalar random slope. By deriving an analytical marginalization, the marginal likelihood is reduced to a one-dimensional integral, circumventing computationally intensive high-dimensional numerical integration. The work establishes conditions for model identifiability and develops associated asymptotic theory. Simulation studies demonstrate excellent numerical stability and favorable finite-sample performance. Application to sandhopper orientation data confirms the validity and practical utility of the proposed approach for variance component inference.

This work addresses the limitations of traditional Gaussian assumptions in accurately representing complex uncertainties, which often lead to information loss and reduced accuracy in multi-stage measurement and control processes. To overcome these challenges, the paper proposes a scalable precision framework based on Gaussian Mixture Models (GMMs), leveraging GMMs as universal approximators of probability density functions. The approach integrates closed-form uncertainty propagation algorithms with memory-efficient computational strategies, thereby transcending the representational constraints of Gaussian methods while maintaining computational tractability. Experimental evaluations in manufacturing and metrology scenarios—such as circular factories—demonstrate that the proposed method significantly enhances the fidelity of uncertainty characterization and propagation, outperforming conventional Gaussian-based techniques.

Existing methods struggle to effectively model the joint dependence between discrete circular variables—such as finitely many equally spaced directional observations—and continuous linear variables. This work proposes the first analytically tractable joint model, employing a wrapped symmetric geometric distribution for the discrete circular component and a Weibull distribution for the linear component, with their dependence structure induced via a trigonometric linking function. The model yields closed-form marginal and conditional distributions along with conditional moments, offers clear theoretical interpretations of its parameters, and establishes monotonicity of the conditional mean and variance with respect to the dependence parameter. Moreover, it enables direct sampling through the inverse transform method. Simulation studies demonstrate excellent parameter estimation performance, and applications to two real-world environmental datasets underscore the model’s effectiveness and practical utility.

Existing approaches, such as those based on the von Mises–Fisher (vMF) distribution, model only the mean direction and thus fail to capture complex geometric structures—such as multimodality, axial symmetry, or zonal patterns—in spherical weighted empirical measures. This work proposes a Geometric Information Decomposition (GID) framework that leverages spherical harmonics to construct a nested sequence of maximum-entropy projections, hierarchically quantifying the incremental information-theoretic gaps at each level. For the first time, this enables a layered decomposition of higher-order geometric structures inherent in spherical measures, transcending the limitations of single-parameter models by fully characterizing features ranging from the mean direction to high-order anisotropy and fine angular patterns. Theoretical guarantees include invariance, consistency, and asymptotic normality, along with a quadratic-form zero-calibration test. Experiments on circular and spherical data successfully reveal latent structures invisible to vMF-based methods, demonstrating the approach’s efficacy and practical utility.

This study addresses the challenge of inefficient inference in Gaussian processes for sequential signal processing by moving beyond the conventional machine learning reliance on independent and identically distributed assumptions. It proposes a unified sequential inference framework for Gaussian processes, systematically integrating techniques from sequential Bayesian inference, incremental learning, streaming computation, and state-space modeling, with signal processing as the central organizing principle. This work not only bridges the longstanding gap between modern machine learning and classical signal processing but also delivers scalable and efficient practical solutions—along with a clear deployment roadmap—for time-series forecasting, anomaly detection, adaptive sensing, and real-time Bayesian optimization.