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Pre-processing for approximate Bayesian computation in image analysis
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Moores, Matthew T., Drovandi, Christopher C., Mengersen, Kerrie and Robert, Christian P. (2015) Pre-processing for approximate Bayesian computation in image analysis. Statistics and Computing, 25 (1). pp. 23-33. doi:10.1007/s11222-014-9525-6 ISSN 0960-3174.
An open access version can be found in:
Official URL: http://dx.doi.org/10.1007/s11222-014-9525-6
Abstract
Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. Images encountered in real world applications can have millions of pixels, therefore scalability is a major concern. We apply ABC with a synthetic likelihood to the hidden Potts model with additive Gaussian noise. Using a pre-processing step, we fit a binding function to model the relationship between the model parameters and the synthetic likelihood parameters. Our numerical experiments demonstrate that the precomputed binding function dramatically improves the scalability of ABC, reducing the average runtime required for model fitting from 71 h to only 7 min. We also illustrate the method by estimating the smoothing parameter for remotely sensed satellite imagery. Without precomputation, Bayesian inference is impractical for datasets of that scale.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Statistics and Computing | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0960-3174 | ||||||||
Official Date: | January 2015 | ||||||||
Dates: |
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Volume: | 25 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 23-33 | ||||||||
DOI: | 10.1007/s11222-014-9525-6 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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