Modified Pólya-Gamma data augmentation for Bayesian analysis of directional data

Abstract

In this work, we develop new data augmentation algorithms for Bayesian analysis of directional data using the von Mises-Fisher distribution in arbitrary dimensions. The approach leads to a new class of distributions, called the Modified Pólya-Gamma distribution, which we construct in detail. The proposed data augmentation strategies circumvent the need for analytic approximations to integration, numerical integration, or Metropolis-Hastings for the corresponding posterior inference. Simulations and real data examples are presented to demonstrate the applicability and to apprise the performance of the proposed procedures.

Keywords:

• Data augmentation algorithm
• directional data
• von Mises-Fisher distribution
• latent variables
• Modified-Half-Normal
• Modified Pólya-Gamma
• infinite convolutions of exponential distributions

MSC2020 subject classifications:

• Primary 62H11
• 62F15
• secondary 33C10
• 60E05

Disclosure statement

No potential conflict of interest was reported by the author(s).