Many models of interest in the natural and social sciences have no
closed-form likelihood function, which means that they cannot be treated using
the usual techniques of statistical inference. In the case where such models
can be efficiently simulated, Bayesian inference is still possible thanks to
the Approximate Bayesian Computation (ABC) algorithm. Although many refinements
have been suggested, ABC inference is still far from routine. ABC is often
excruciatingly slow due to very low acceptance rates. In addition, ABC requires
introducing a vector of "summary statistics", the choice of which is relatively
arbitrary, and often require some trial and error, making the whole process
quite laborious for the user.
We introduce in this work the EP-ABC algorithm, which is an adaptation to the
likelihood-free context of the variational approximation algorithm known as
Expectation Propagation (Minka, 2001). The main advantage of EP-ABC is that it
is faster by a few orders of magnitude than standard algorithms, while
producing an overall approximation error which is typically negligible. A
second advantage of EP-ABC is that it replaces the usual global ABC constraint
on the vector of summary statistics computed on the whole dataset, by n local
constraints of the form that apply separately to each data-point. As a
consequence, it is often possible to do away with summary statistics entirely.
In that case, EP-ABC approximates directly the evidence (marginal likelihood)
of the model.
Comparisons are performed in three real-world applications which are typical
of likelihood-free inference, including one application in neuroscience which
is novel, and possibly too challenging for standard ABC techniques.

介绍了 EP-ABC 算法，它是期望传播算法在无似然函数情况下的一种适应性算法，它具有比标准算法更快的速度和更高的精度，并且可以在没有总结统计的情况下直接逼近模型的证据。