Learning Functions and Approximate Bayesian Computation Design: ABCD

Entropy

Markus Hainy¹  Werner G. Müller¹ 

[1] Department of Applied Statistics, Johannes Kepler University, 4040 Linz, Austria; E-Mails:

关键词: learning;    Shannon information;    majorization;    optimum experimental design;    approximate Bayesian computation;   

DOI  :  10.3390/e16084353

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland