統計数理研究所

講演題目: Circular statistics for modeling linear and non-linear data on 3-smooth manifolds

概要: There is a paucity of probability distributions for modeling linear data with high volatility. So is true for models for directional data which are amenable to statistical inference. We start with the univariate case, i. e. data defined on the circle or circular data. Several approaches including Stereographic Projection, Maximum Entropy and Wrapping are discussed. We show how Mobius transformation and Stereographic projection can lead to elegant probability distributions from the line to the circle and vis-a-vis.
This opens up a new approach to modeling high-volatility data, as encountered in finance and stock markets. For the bivariate case, specifically for random variables defined on 3-smooth manifolds, torus and cylinder, several unified approaches, e.g. bivariate Fourier series, maximum entropy and conditional specifications, are enhanced. These lead to interesting applications of special functions in both linear and trigonometric arguments, including confluent hypergeometric functions and Bessel functions. Regression models and Classification rules for such directional data are presented. Real-life applications of these distributions to applied sciences, e.g. agricultural, biological, defence, environmental, etc. sciences are briefly illustrated.