Bayesian Estimation of the Degrees of Freedom Parameter of the Student-$t$ Distribution---A Beneficial Re-parameterization

Darjus Hosszejni

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arXiv · 2109.01726

Bayesian Estimation of the Degrees of Freedom Parameter of the Student-$t$ Distribution---A Beneficial Re-parameterization

Darjus Hosszejni

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Abstract

In this paper, conditional data augmentation (DA) is investigated for the degrees of freedom parameter $ν$ of a Student-$t$ distribution. Based on a restricted version of the expected augmented Fisher information, it is conjectured that the ancillarity DA is progressively more efficient for MCMC estimation than the sufficiency DA as $ν$ increases; with the break even point lying at as low as $ν\approx4$. The claim is examined further and generalized through a large simulation study and a application to U.S. macroeconomic time series. Finally, the ancillarity-sufficiency interweaving strategy is empirically shown to combine the benefits of both DAs. The proposed algorithm may set a new standard for estimating $ν$ as part of any model.

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BibTeX RIS

Darjus Hosszejni. 2021-09-03. Bayesian Estimation of the Degrees of Freedom Parameter of the Student-$t$ Distribution---A Beneficial Re-parameterization. https://arxiv.org/abs/2109.01726

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