Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain Monte Carlo ones. Nonetheless, introducing appropriate auxiliary variables while preserving the initial target probability distribution and offering a computationally efficient inference cannot be conducted in a systematic way. To deal with such issues, this paper studies a unified framework, coined asymptotically exact data augmentation (AXDA), which encompasses both well-established and more recent approximate augmented models. In a broader perspective, this paper shows that AXDA models can benefit from interesting statistical properties and yield efficient inference algorithms. In non-asymptotic settings, the quality of the proposed approximation is assessed with several theoretical results. The latter are illustrated on standard statistical problems. Supplementary materials including computer code for this paper are available online.

中文翻译：

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渐近精确的数据增强：模型、属性和算法

通过引入辅助变量，数据增强已成为一种普遍存在的技术，以提高收敛性、简化实现或减少诸如马尔可夫链蒙特卡罗等推理方法的计算时间。尽管如此，在保留初始目标概率分布并提供计算高效推理的同时引入适当的辅助变量无法以系统的方式进行。为了解决这些问题，本文研究了一个统一的框架，创造了渐近精确数据增强（AXDA），它包括完善的和最近的近似增强模型。从更广泛的角度来看，本文表明 AXDA 模型可以受益于有趣的统计特性并产生有效的推理算法。在非渐近环境中，建议的近似的质量是通过几个理论结果来评估的。后者在标准统计问题上进行了说明。包括本文计算机代码在内的补充材料可在线获取。