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Sampling-Based Accuracy Testing of Posterior Estimators for General Inference

P Lemos, A Coogan, Y Hezaveh… - arXiv preprint arXiv …, 2023 - arxiv.org
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… Posterior inference with generative models is an alternative to methods such as Markov Chain Monte Carlo, both for likelihood-based and simulation-based inference. …

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BibTeX

@article{2302.03026v2,
Author        = {Pablo Lemos and Adam Coogan and Yashar Hezaveh and Laurence Perreault-Levasseur},
Title         = {Sampling-Based Accuracy Testing of Posterior Estimators for General Inference},
Eprint        = {2302.03026v2},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.ML},
Abstract      = {Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.},
Year          = {2023},
Month         = {Feb},
Url           = {http://arxiv.org/abs/2302.03026v2},
File          = {2302.03026v2.pdf}
}

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