Title: Bayesian inference for mode preserving distributions on the circle
Authors: Toshihiro Abe - Nanzan University (Japan)
Yoichi Miyata - Takasaki City University of Economics (Japan)
Takayuki Shiohama - Tokyo University of Science (Japan) [presenting]
Abstract: Unimodal skew circular distributions through inverse monotone functions are considered. General properties of the distributions together with skewness measures based on the distribution and density functions are provided. The inverse $k$-sine-skewed circular distributions are introduced as special cases of this type. More flat-topped and sharply peaked version of the distributions are also given. General results are also provided for maximum likelihood estimation (MLE) of the parameters and Fisher information matrix of the distributions. To calculate Bayes estimates for the model parameters, we introduce the importance sampling estimation algorithms. We also provide approximate Bayes estimates using Lindley's approximation based on both MLE and MAP estimates. Monte Carlo simulations are performed to compare the performance of the Bayes estimates with the classical estimates. Three circular datasets are analyzed for illustrative purposes.