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Pre-processing for approximate Bayesian computation in image analysis

Journal Article


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.

Authors


  •   Moores, Matt T.
  •   Drovandi, Christopher C. (external author)
  •   Mengersen, Kerrie (external author)
  •   Robert, Christian P. (external author)

Publication Date


  • 2015

Citation


  • Moores, M. T., Drovandi, C. C., Mengersen, K. & Robert, C. P. (2015). Pre-processing for approximate Bayesian computation in image analysis. Statistics and Computing, 25 (1), 23-33.

Scopus Eid


  • 2-s2.0-84925517418

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1680

Number Of Pages


  • 10

Start Page


  • 23

End Page


  • 33

Volume


  • 25

Issue


  • 1

Place Of Publication


  • United States

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.

Authors


  •   Moores, Matt T.
  •   Drovandi, Christopher C. (external author)
  •   Mengersen, Kerrie (external author)
  •   Robert, Christian P. (external author)

Publication Date


  • 2015

Citation


  • Moores, M. T., Drovandi, C. C., Mengersen, K. & Robert, C. P. (2015). Pre-processing for approximate Bayesian computation in image analysis. Statistics and Computing, 25 (1), 23-33.

Scopus Eid


  • 2-s2.0-84925517418

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1680

Number Of Pages


  • 10

Start Page


  • 23

End Page


  • 33

Volume


  • 25

Issue


  • 1

Place Of Publication


  • United States