Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve mixing/convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain Monte Carlo. Nonetheless, introducing appropriate auxiliary variables while preserving the initial target probability distribution cannot be conducted in a systematic way but highly depends on the considered problem. To deal with such issues, this paper draws a unified framework, namely asymptotically exact data augmentation (AXDA), which encompasses several well-established but also more recent approximate augmented models. Benefiting from a much more general perspective, it delivers some additional qualitative and quantitative insights concerning these schemes. In particular, general properties of AXDA along with non-asymptotic theoretical results on the approximation that is made are stated. Close connections to existing Bayesian methods (e.g. mixture modeling, robust Bayesian models and approximate Bayesian computation) are also drawn. All the results are illustrated with examples and applied to standard statistical learning problems.

介绍了一种名为 AXDA 的数据增强统一框架，其中包括一些较新的近似增强模型，研究显示 AXDA 模型可以从有趣的统计性质中获益，并产生有效的推断算法。

渐近准确的数据增广：模型、属性与算法