Semiparametric Bayesian Method for High-Dimensional Spherical Data

• Activity Number: 534
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Thomas Jiang*
• Companies: National Chengchi University
• Keywords: high-dimensional spherical data ; Ferguson-Dirichlet process ; von Mises-Fisher distribution ; Bayesian predictive density ; Bayesian two-sample test

Abstract

In addition to two or three dimensional spherical data, in many scientific problems, the measured observations are seen or treated as high dimensional spherical data. For example, in machine learning problems, one may need to analyze data, which are likely in the form of n-dimensional ball (see, e.g., Banerjee et al. (2005)). The spherical data problems usually cannot be seen in the same way as those of the regular data. Here, we provide general semi-parametric Bayesian method for making statistical inferences on high dimensional spherical data. This generalizes those for two or three dimensional data. In particular, we show how to use our semi-parametric method to give the Bayesian predictive density and to test whether two samples are from two populations with the same mean. A von Mises-Fisher distribution is shown to be conjugate for the high dimensional von Mises-Fisher distribution data. This makes the analyses of high dimensional spherical data easier in computation.