  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.
