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What are the lesser-known but powerful probabilistic inference algorithms?

Most references about probabilistic graphical models describe popular inference methods like Variable Elimination and Junction Tree. However, I think that there are a huge number of other important probabilistic inference algorithms out there. Every once in a while I would stumble upon a paper that describes a method that I didn't hear about before, take for example The Factored Frontier Algorithm for Approximate Inference in DBNs.

Please try to add one algorithm per answer, with a brief description or points to related papers.

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    $\begingroup$ While I think it's an interesting topic, shopping list questions are generally discouraged. $\endgroup$ – Marc Claesen Oct 20 '15 at 13:27
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Indirect inference

According to The New Palgrave Dictionary of Economics, Second Edition (entry by Anthony A. Smith, Jr),

Indirect inference is a simulation-based method for estimating the parameters of economic models. Its hallmark is the use of an auxiliary model to capture aspects of the data upon which to base the estimation. The parameters of the auxiliary model can be estimated using either the observed data or data simulated from the economic model. Indirect inference chooses the parameters of the economic model so that these two estimates of the parameters of the auxiliary model are as close as possible. The auxiliary model need not be correctly specified; when it is, indirect inference is equivalent to maximum likelihood.

Another (more technical) reference is Gourieroux et al. "Indirect inference" (1993) in the Journal of Applied Econometrics, 8(S1). Indirect inference is also mentioned in the thread "Parameter Estimation for intractable Likelihoods / Alternatives to approximate Bayesian computation".

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