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A Strategy for Bayesian Inference for Computationally Expensive Models with Application to the Estimation of Stem Cell Properties
Author(s) -
Overstall Antony M.,
Woods David C.
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.12017
Subject(s) - computer science , inference , markov chain monte carlo , bayesian inference , bayesian probability , statistical inference , gaussian process , approximate bayesian computation , likelihood function , machine learning , algorithm , artificial intelligence , gaussian , estimation theory , mathematics , statistics , physics , quantum mechanics
Summary Bayesian inference is considered for statistical models that depend on the evaluation of a computationally expensive computer code or simulator. For such situations, the number of evaluations of the likelihood function, and hence of the unnormalized posterior probability density function, is determined by the available computational resource and may be extremely limited. We present a new example of such a simulator that describes the properties of human embryonic stem cells using data from optical trapping experiments. This application is used to motivate a novel strategy for Bayesian inference which exploits a Gaussian process approximation of the simulator and allows computationally efficient Markov chain Monte Carlo inference. The advantages of this strategy over previous methodology are that it is less reliant on the determination of tuning parameters and allows the application of model diagnostic procedures that require no additional evaluations of the simulator. We show the advantages of our method on synthetic examples and demonstrate its application on stem cell experiments.