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Entropy 2014, 16(8), 4353-4374; doi:10.3390/e16084353

Learning Functions and Approximate Bayesian Computation Design: ABCD

Department of Applied Statistics, Johannes Kepler University, 4040 Linz, Austria
Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK
Author to whom correspondence should be addressed.
Received: 25 April 2014 / Revised: 18 July 2014 / Accepted: 28 July 2014 / Published: 4 August 2014
(This article belongs to the Special Issue Entropy in Experimental Design, Sensor Placement, Inquiry and Search)
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A general approach to Bayesian learning revisits some classical results, which study which functionals on a prior distribution are expected to increase, in a preposterior sense. The results are applied to information functionals of the Shannon type and to a class of functionals based on expected distance. A close connection is made between the latter and a metric embedding theory due to Schoenberg and others. For the Shannon type, there is a connection to majorization theory for distributions. A computational method is described to solve generalized optimal experimental design problems arising from the learning framework based on a version of the well-known approximate Bayesian computation (ABC) method for carrying out the Bayesian analysis based on Monte Carlo simulation. Some simple examples are given. View Full-Text
Keywords: learning; Shannon information; majorization; optimum experimental design; approximate Bayesian computation learning; Shannon information; majorization; optimum experimental design; approximate Bayesian computation

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Hainy, M.; Müller, W.G.; P. Wynn, H. Learning Functions and Approximate Bayesian Computation Design: ABCD. Entropy 2014, 16, 4353-4374.

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