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Circular Data Modelling

PhD project: Kees Mulder

Bayesian circular models in the intrinsic approach

Kees Mulder’s project employs the intrinsic approach in circular data modeling, which focuses on distributions defined directly on the circle, such as the von Mises distribution. These models have simpler form than many other circular data models, but face a multitude of practical problems. Some sub-projects have included:

  • Bayesian circular outcome regression models, which follow the GLM-like approach by Fisher & Lee (1992).The Bayesian variant allows more extensive analyses and interpretation than the original formulation and solves several major practical problems. The associated package was published on CRAN and can also be found on GitHub.
  • Bayesian hypothesis tests for circular data, in particular uniformity, by means of a Bayes Factor.
  • Flexible (in particular peaked) mixture models for saccade directions. Eye movement directions often have peaked distributions, which can be naturally modeled by mixtures of peaked circular distributions, in this case Batschelet-type. These analyses can be found in this GitHub package.
  • Interpretation of projected normal regression models.
  • MCMC sampling for the Jones-Pewsey distribution.
  • Circular Mediation models.
  • Censored data on the circle.

In general, code for this project is available on GitHub.