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Abstract:
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Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottle-neck. There is also no consensus as to how to best assess the performance of such methods. We show how a nonparametric conditional density estimation (CDE) framework can help address three key challenges in ABC, namely: (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to compare the performance of ABC and related methods with CDE as a goal, and (iii) how to efficiently choose among a very large set of summary statistic based on a CDE loss. We provide both theoretical and empirical evidence to justify the use of such procedures and describe settings where standard ABC may fail.
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