TY - UNPB
T1 - Bayesian Estimation of the Degrees of Freedom Parameter of the Student-t Distribution—A Beneficial Re-parameterization
AU - Hosszejni, Darjus
PY - 2021
Y1 - 2021
N2 - 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≈4. 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.
AB - 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≈4. 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.
U2 - 10.48550/arXiv.2109.01726
DO - 10.48550/arXiv.2109.01726
M3 - Working Paper/Preprint
BT - Bayesian Estimation of the Degrees of Freedom Parameter of the Student-t Distribution—A Beneficial Re-parameterization
PB - arXiv
ER -