Pre-processing for approximate Bayesian computation in image analysis

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 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.

5th IMS-ISBA joint meeting (MCMSki IV)

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Cited by in corpus (7)

• On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
• Variational Bayes with Synthetic Likelihood
• A Survey of Bayesian Statistical Approaches for Big Data
• Component-wise approximate Bayesian computation via Gibbs-like steps
• Approximating the Likelihood in Approximate Bayesian Computation
• Adaptive ABC model choice and geometric summary statistics for hidden Gibbs random fields
• Bayesian quantification for coherent anti-Stokes Raman scattering spectroscopy