  We are living in the big data era, as current technologies and networks allow
for the easy and routine collection of data sets in different disciplines.
Bayesian Statistics offers a flexible modeling approach which is attractive for
describing the complexity of these datasets. These models often exhibit a
likelihood function which is intractable due to the large sample size, high
number of parameters, or functional complexity. Approximate Bayesian
Computational (ABC) methods provides likelihood-free methods for performing
statistical inferences with Bayesian models defined by intractable likelihood
functions. The vastity of the literature on ABC methods created a need to
review and relate all ABC approaches so that scientists can more readily
understand and apply them for their own work. This article provides a unifying
review, general representation, and classification of all ABC methods from the
view of approximate likelihood theory. This clarifies how ABC methods can be
characterized, related, combined, improved, and applied for future research.
Possible future research in ABC is then suggested.
