In this paper, conditional data augmentation (DA) is investigated for the degrees of freedom parameter $\nu$ 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 $\nu$ increases; with the break even point lying at as low as $\nu\approx4$. 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 $\nu$ as part of any model.

翻译：在本文中,对有条件的数据增强(DA)进行调查,以了解学生-美元分配的自由参数度为$\nu$美元。根据限制版的预期增加的渔业信息,可以推测,对于MCMC估计而言,异常度DA比充足度DA增加$\nu$增加的充足性DA越来越有效;断裂点低至$\nu\approx4美元;通过大规模模拟研究和对美国宏观经济时间序列的应用,对索赔进行进一步和普及审查。最后,从经验上表明,对等性-充足互交战略结合了两个DA的效益。提议的算法可能为估算作为任何模型一部分的$\nu美元设定新的标准。