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

Subhadip Pal; Jeremy Gaskins

doi:10.1080/00949655.2022.2067853

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

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	3430-3451
Number of pages	22
Journal	Journal of Statistical Computation and Simulation
Volume	92
Issue number	16
DOIs	https://doi.org/10.1080/00949655.2022.2067853
Publication status	Published - 2022
Externally published	Yes

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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10.1080/00949655.2022.2067853

Cite this

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title = "Modified P{\'o}lya-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 P{\'o}lya-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.",

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AB - 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.

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KW - Modified-Half-Normal

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KW - secondary 33C10

KW - von Mises-Fisher distribution

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

Abstract

Keywords

ASJC Scopus subject areas

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