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

Subhadip Pal, Jeremy Gaskins

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)3430-3451
Number of pages22
JournalJournal of Statistical Computation and Simulation
Volume92
Issue number16
DOIs
Publication statusPublished - 2022
Externally publishedYes

Keywords

  • 60E05
  • 62F15
  • Data augmentation algorithm
  • directional data
  • infinite convolutions of exponential distributions
  • latent variables
  • Modified Pólya-Gamma
  • Modified-Half-Normal
  • Primary 62H11
  • secondary 33C10
  • von Mises-Fisher distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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