GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation. Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging. The Approximate Bayesian Computation (ABC) framework is the standard statistical tool to handle these likelihood free problems, but they require a very large number of simulations. In this work we develop two new ABC sampling algorithms that significantly reduce the number of simulations necessary for posterior inference. Both algorithms use confidence estimates for the accept probability in the Metropolis Hastings step to adaptively choose the number of necessary simulations. Our GPS-ABC algorithm stores the information obtained from every simulation in a Gaussian process which acts as a surrogate function for the simulated statistics. Experiments on a challenging realistic biological problem illustrate the potential of these algorithms.

References in zbMATH (referenced in 15 articles )

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  1. Moores, Matthew; Nicholls, Geoff; Pettitt, Anthony; Mengersen, Kerrie: Scalable Bayesian inference for the inverse temperature of a hidden Potts model (2020)
  2. Spiliopoulos, Konstantinos: Information geometry for approximate Bayesian computation (2020)
  3. Järvenpää, Marko; Gutmann, Michael U.; Pleska, Arijus; Vehtari, Aki; Marttinen, Pekka: Efficient acquisition rules for model-based approximate Bayesian computation (2019)
  4. Drovandi, Christopher C.; Moores, Matthew T.; Boys, Richard J.: Accelerating pseudo-marginal MCMC using Gaussian processes (2018)
  5. Fasiolo, Matteo; Wood, Simon N.; Hartig, Florian; Bravington, Mark V.: An extended empirical saddlepoint approximation for intractable likelihoods (2018)
  6. Järvenpää, Marko; Gutmann, Michael U.; Vehtari, Aki; Marttinen, Pekka: Gaussian process modelling in approximate Bayesian computation to estimate horizontal gene transfer in bacteria (2018)
  7. Karabatsos, George; Leisen, Fabrizio: An approximate likelihood perspective on ABC methods (2018)
  8. McKinley, Trevelyan J.; Vernon, Ian; Andrianakis, Ioannis; McCreesh, Nicky; Oakley, Jeremy E.; Nsubuga, Rebecca N.; Goldstein, Michael; White, Richard G.: Approximate Bayesian computation and simulation-based inference for complex stochastic epidemic models (2018)
  9. Ong, Victor M. H.; Nott, David J.; Tran, Minh-Ngoc; Sisson, Scott A.; Drovandi, Christopher C.: Variational Bayes with synthetic likelihood (2018)
  10. Ong, Victor M.-H.; Nott, David J.; Tran, Minh-Ngoc; Sisson, Scott A.; Drovandi, Christopher C.: Likelihood-free inference in high dimensions with synthetic likelihood (2018)
  11. Hepler, Staci A.; Herbei, Radu: A Monte Carlo approach to quantifying discrepancies between intractable posterior distributions (2017)
  12. Shelton, Jacquelyn A.; Gasthaus, Jan; Dai, Zhenwen; Lücke, Jörg; Gretton, Arthur: GP-Select: accelerating EM using adaptive subspace preselection (2017)
  13. Zhang, Cheng; Shahbaba, Babak; Zhao, Hongkai: Hamiltonian Monte Carlo acceleration using surrogate functions with random bases (2017)
  14. Gutmann, Michael U.; Corander, Jukka: Bayesian optimization for likelihood-free inference of simulator-based statistical models (2016)
  15. Prangle, Dennis: Lazy ABC (2016)