Title: Shrinkage priors on complex statistical manifolds
Authors: Hidemasa Oda - The University of Tokyo (Japan) [presenting]
Fumiyasu Komaki - The University of Tokyo (Japan)
Abstract: It is difficult to define the best properties that statistical manifolds should possess. One of the good properties we believe statistical manifolds have is their Kaehler structure. Complex-valued stochastic processes are useful models for parametrizing complex or bivariate signals. We expanded the theory of $\alpha$-geometry of real time series for complex time series. For most of the parts, generalized results of real time series for complex time series are obtained. We are interested in particular in the case when the information manifold is a Kaehler manifold. It has been previously shown that the information geometry of complex time series is Kaehler. We further investigate the structure of the complex autoregressive models and its positive superharmonic priors. We expect that Ricci-free $\alpha$-Kaehler structure has an important role in the theory of complex information geometry. We will discuss the application of $\alpha$-Kaehler geometry for general complex linear systems.