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Adaptive Gaussian process approximation for Bayesian inference with expensive likelihood functions

29 Mar 2017arXiv:1703.09930archive 2025-07-28

Hongqiao Wang, Jinglai Li

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we write the joint density approximately as a product of an approximate posterior density and an exponentiated GP surrogate. We then provide an adaptive algorithm to construct such an approximation, where an active learning method is used to choose the design points. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for Bayesian computation.

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AGPUtility dflemin3/approxposterior/approxposterior/utility.py community (archive-listed) unverified MIT (permissive) · 404832bb9efd503a · report
batchMeansMCSE dflemin3/approxposterior/approxposterior/mcmcUtils.py community (archive-listed) unverified MIT (permissive) · 68dc102046756dc4 · report
defaultHyperPrior dflemin3/approxposterior/approxposterior/gpUtils.py community (archive-listed) unverified MIT (permissive) · 8f99907a49c753ee · report
estimateBurnin dflemin3/approxposterior/approxposterior/mcmcUtils.py community (archive-listed) unverified MIT (permissive) · 7e35680d464345d9 · report
fitGMM dflemin3/approxposterior/approxposterior/gmmUtils.py community (archive-listed) unverified MIT (permissive) · 730cf0ac1f9e83db · report
get_lnprior dflemin3/approxposterior/approxposterior/priors.py community (archive-listed) unverified MIT (permissive) · 680335e98e9a9732 · report
get_prior_unit_cube dflemin3/approxposterior/approxposterior/priors.py community (archive-listed) unverified MIT (permissive) · a8b51ed0a04cc045 · report
get_theta_bounds dflemin3/approxposterior/approxposterior/priors.py community (archive-listed) unverified MIT (permissive) · ef5bd670280bc601 · report
klNumerical dflemin3/approxposterior/approxposterior/utility.py community (archive-listed) unverified MIT (permissive) · 50179160b6ef4256 · report
logsubexp dflemin3/approxposterior/approxposterior/utility.py community (archive-listed) unverified MIT (permissive) · 26944f8d426fd1fb · report
optimizeGP dflemin3/approxposterior/approxposterior/gpUtils.py community (archive-listed) unverified MIT (permissive) · 319d023f8c651ea5 · report
rosenbrockLnlike dflemin3/approxposterior/approxposterior/likelihood.py community (archive-listed) unverified MIT (permissive) · dfcead43c44688d3 · report
rosenbrockLnprior dflemin3/approxposterior/approxposterior/likelihood.py community (archive-listed) unverified MIT (permissive) · da6e08d2a6bcd72d · report
rosenbrockSample dflemin3/approxposterior/approxposterior/likelihood.py community (archive-listed) unverified MIT (permissive) · bb5488c38e4e2fc0 · report
validateMCMCKwargs dflemin3/approxposterior/approxposterior/mcmcUtils.py community (archive-listed) unverified MIT (permissive) · 43ac8a0fc5abfea6 · report

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Active LearningBayesian Inference

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Gaussian Process

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