Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an ε-ball around the observed data, which is only correct in the limit ε 0. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters.

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However, practical posteriors are often, even locally, highly non-Gaussian, and empirical performance deteriorates.

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This view enables a structured variational approximation capturing dependencies across variables in the model.