Learning functions and approximate Bayesian computation design: ABCD

Hainy, M., Müller, W.G and Wynn, Henry P. ORCID: 0000-0002-6448-1080 (2014) Learning functions and approximate Bayesian computation design: ABCD. Entropy, 16 (8). pp. 4353-4374. ISSN 1099-4300

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Abstract

Interventions aimed at high-need families have difficulty demonstrating short-term impact on child behaviour. 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.

Item Type:	Article
Official URL:	http://www.mdpi.com/journal/entropy
Additional Information:	© 2014 Authors, licensee MDPI, Basel, Switzerland © CC BY 3.0
Divisions:	LSE
Subjects:	T Technology > T Technology (General) T Technology > TJ Mechanical engineering and machinery
Date Deposited:	05 Sep 2014 08:56
Last Modified:	12 Dec 2024 00:42
Projects:	I-833-N18
Funders:	French Science Fund (ANR), Austrian Science Fund (FWF), Exzellenzstipendium des Landes Oberösterreich
URI:	http://eprints.lse.ac.uk/id/eprint/59283

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