Pre-processing for approximate Bayesian computation in image analysis
Moores, Matthew T., Drovandi, Christopher C., Mengersen, Kerrie, & Robert, Christian P. (2015) Pre-processing for approximate Bayesian computation in image analysis. Statistics and Computing, 25(1), pp. 23-33.
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 hours to only 7 minutes. 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.
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|Item Type:||Journal Article|
|Additional Information:||Published online: 09 December 2014|
|Keywords:||Approximate Bayesian Computation, Hidden Markov random field, Indirect inference, Potts/Ising model, Quasi-likelihood, Sequential Monte Carlo|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)|
|Divisions:||Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2014 Springer Science+Business Media|
|Copyright Statement:||The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-014-9525-6|
|Deposited On:||23 Dec 2014 05:32|
|Last Modified:||04 Jan 2016 02:15|
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