Approximate Bayesian computation (ABC) gives exact results under the assumption of model error
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Richard David Wilkinson
Abstract
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data sets from the model. In this paper we show that under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used. This interpretation allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work. ABC algorithms can be generalized by replacing the 0–1 cut-off with an acceptance probability that varies with the distance of the simulated data from the observed data. The acceptance density gives the distribution of the error term, enabling the uniform error usually used to be replaced by a general distribution. This generalization can also be applied to approximate Markov chain Monte Carlo algorithms. In light of this work, ABC algorithms can be seen as calibration techniques for implicit stochastic models, inferring parameter values in light of the computer model, data, prior beliefs about the parameter values, and any measurement or model errors.
I would like to thank Professor Paul Blackwell for his suggestion that the metric in the ABC algorithm might have a probabilistic interpretation. I would also like to thank Professor Simon Tavaré, Professor Tony O’Hagan, and Dr Jeremy Oakley for useful discussions on an early draft of the manuscript.
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©2013 by Walter de Gruyter Berlin Boston
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Artikel in diesem Heft
- Approximate Bayesian computation (ABC) gives exact results under the assumption of model error
- Modeling the DNA copy number aberration patterns in observational high-throughput cancer data
- Exploring the sampling universe of RNA-seq
- Detection of epigenetic changes using ANOVA with spatially varying coefficients
- Robustness of chemometrics-based feature selection methods in early cancer detection and biomarker discovery
- Recursively partitioned mixture model clustering of DNA methylation data using biologically informed correlation structures
- A novel method for analyzing genetic association with longitudinal phenotypes
- Two optimization strategies of multi-stage design in clinical proteomic studies
