Generalized Bayesian Computation



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Just saw a presentation of Dellaporta et al. (2022).

I am not sure how any of the results are specific to that very impressive paper, but she attributes prior work to Fong, Lyddon, and Holmes (2019); Lyddon, Walker, and Holmes (2018); Matsubara et al. (2021); Pacchiardi and Dutta (2022); Schmon, Cannon, and Knoblauch (2021). Combines bootstrap, Bayes nonparametrics, MMD, simulation based inference in an M-open setting.

Clearly there is some interesting stuff going on here. Perhaps this introductory post will be a good start: Generalizing Bayesian Inference.

References

Dellaporta, Charita, Jeremias Knoblauch, Theodoros Damoulas, and François-Xavier Briol. 2022. Robust Bayesian Inference for Simulator-Based Models via the MMD Posterior Bootstrap.” arXiv:2202.04744 [Cs, Stat], February.
Fong, Edwin, Simon Lyddon, and Chris Holmes. 2019. Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior Bootstrap.” arXiv:1902.03175 [Cs, Stat], August.
Galvani, Marta, Chiara Bardelli, Silvia Figini, and Pietro Muliere. 2021. A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap.” Algorithms 14 (1): 11.
Lyddon, Simon, Stephen Walker, and Chris Holmes. 2018. Nonparametric Learning from Bayesian Models with Randomized Objective Functions.” In Proceedings of the 32nd International Conference on Neural Information Processing Systems, 2075–85. NIPS’18. Red Hook, NY, USA: Curran Associates Inc.
Matsubara, Takuo, Jeremias Knoblauch, François-Xavier Briol, and Chris J. Oates. 2021. Robust Generalised Bayesian Inference for Intractable Likelihoods.” arXiv:2104.07359 [Math, Stat], April.
Pacchiardi, Lorenzo, and Ritabrata Dutta. 2022. Generalized Bayesian Likelihood-Free Inference Using Scoring Rules Estimators.” arXiv:2104.03889 [Stat], March.
Schmon, Sebastian M., Patrick W. Cannon, and Jeremias Knoblauch. 2021. Generalized Posteriors in Approximate Bayesian Computation.” arXiv:2011.08644 [Stat], February.

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