Directional
Statistics

RESEARCH / BAYESIAN DIRECTIONAL STATISTICS

Research on
circular models.

Priors that express directional variation, regression for angular responses, and joint circular models that connect direction with other quantities.

PRIORSCIRCULAR RESPONSECIRCULAR COVARIATE

01 / RESEARCH TOPICS

Three connected questions.

01
π(κ)

Priors for circular models

Penalized complexity priors for the concentration of circular distributions.

Explore the research
02
Y ∈ S¹

Regression with a circular response

Link-adjusted von Mises models for angular outcomes and structured predictors.

Explore the research
03
(Y, θ)

Regression with a circular covariate

Joint circular models connecting direction and a linear response through shared latent structure.

Explore the research

02 / PAPERS

The research in detail.

CIRCULAR PRIORS Penalizing complexity priors for Bayesian inference of circular models

Ye, Van Niekerk & Rue (2026)

CIRCULAR REGRESSION A Bayesian regression framework for circular models with INLA

Ye, Van Niekerk & Rue (2026)

03 / Stan IMPLEMENTATIONS

From models to worked examples.

All three Stan tutorials
01
Priors / Stan IMPLEMENTATION

Penalized Complexity Priors for Circular Distributions

Construct and calibrate PC priors for von Mises concentration, with circular-uniform and point-mass base models.

02
Circular response / Stan IMPLEMENTATION

Circular Distributions for Regression Models

Explore link-adjusted von Mises regression, from fixed effects to temporal structure and wind-direction data.

03
Circular covariate / Stan IMPLEMENTATION

Joint circular models

Explore regression models with circular covariates and learn how to extend them to joint modelling.