Weighted approximate Bayesian computation via Sanov’s theorem

Cecilia Viscardi (), Michele Boreale and Fabio Corradi
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Cecilia Viscardi: Università di Firenze, DiSIA
Michele Boreale: Università di Firenze, DiSIA
Fabio Corradi: Università di Firenze, DiSIA

Computational Statistics, 2021, vol. 36, issue 4, No 16, 2719-2753

Abstract: Abstract We consider the problem of sample degeneracy in Approximate Bayesian Computation. It arises when proposed values of the parameters, once given as input to the generative model, rarely lead to simulations resembling the observed data and are hence discarded. Such “poor” parameter proposals do not contribute at all to the representation of the parameter’s posterior distribution. This leads to a very large number of required simulations and/or a waste of computational resources, as well as to distortions in the computed posterior distribution. To mitigate this problem, we propose an algorithm, referred to as the Large Deviations Weighted Approximate Bayesian Computation algorithm, where, via Sanov’s Theorem, strictly positive weights are computed for all proposed parameters, thus avoiding the rejection step altogether. In order to derive a computable asymptotic approximation from Sanov’s result, we adopt the information theoretic “method of types” formulation of the method of Large Deviations, thus restricting our attention to models for i.i.d. discrete random variables. Finally, we experimentally evaluate our method through a proof-of-concept implementation.

Keywords: ABC; Large deviation theory; Method of types; Sample degeneracy; ESS; Importance sampling (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-021-01093-4

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