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Bayesian Experimental Design for Models with Intractable Likelihoods
Author(s) -
Drovandi Christopher C.,
Pettitt Anthony N.
Publication year - 2013
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12081
Subject(s) - approximate bayesian computation , markov chain monte carlo , computer science , bayesian probability , markov chain , multivariate statistics , population , importance sampling , likelihood function , mathematical optimization , monte carlo method , machine learning , algorithm , estimation theory , artificial intelligence , mathematics , statistics , demography , inference , sociology
Summary In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre‐computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables.