Analysis of circular data in the dynamic model and mixture of von Mises distributions

Analysis of circular data becomes more and more popular in many fields of studies. In this report, I present two statistical analysis of circular data using von Mises distributions. Firstly, the maximization-expectation algorithm is reviewed and used to classify and estimate circular data from the mixture of von Mises distributions. Secondly, Forward Filtering Backward Smoothing method via particle filtering is reviewed and implemented when circular data appears in the dynamic state-space models.