Non-linear regression models for Approximate Bayesian Computation |
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Authors: | Michael G B Blum Olivier François |
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Institution: | (1) Centre National de la Recherche Scientifique, TIMC-IMAG, Faculty of Medicine of Grenoble, 38706 La Tronche, France;(2) Institut National Polytechnique de Grenoble, TIMC-IMAG, Faculty of Medicine of Grenoble, 38706 La Tronche, France |
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Abstract: | Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood
is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality
when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior
density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter
on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared
to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two
examples of inference in statistical genetics and in a queueing model. |
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