# Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior Bootstrap

arXiv: https://arxiv.org/abs/1902.03175 · HTML: https://mlsanity.com/paper/1902.03175/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2019.

## Built on by (most cited first, 16 of 16)

- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
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- [Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularization](https://mlsanity.com/paper/2301.13528/) (2023)
- [Posterior Uncertainty Quantification in Neural Networks using Data Augmentation](https://mlsanity.com/paper/2403.12729/) (2024)
- [AI-Powered Bayesian Inference](https://mlsanity.com/paper/2502.19231/) (2025)
- [Enhancing Transfer Learning with Flexible Nonparametric Posterior Sampling](https://mlsanity.com/paper/2403.07282/) (2024)
- [A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networks](https://mlsanity.com/paper/2303.02637/) (2023)
- [Robust Bayesian Inference for Measurement Error Misspecification: The Berkson and Classical Cases](https://mlsanity.com/paper/2306.01468/) (2023)
- [Generative vs. Discriminative modeling under the lens of uncertainty quantification](https://mlsanity.com/paper/2406.09172/) (2024)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [A Bayesian Non-parametric Approach to Generative Models: Integrating Variational Autoencoder and Generative Adversarial Networks using Wasserstein and Maximum Mean Discrepancy](https://mlsanity.com/paper/2308.14048/) (2023)
- [GEMSS: A Variational Method for Discovering Multiple Sparse Solutions in Classification and Regression Problems](https://mlsanity.com/paper/2602.08913/) (2026)
- [Supercharging Bayesian Inference with Reliable AI-Informed Priors](https://mlsanity.com/paper/2605.09834/) (2026)
- [Nonparametric posterior learning for emission tomography with multimodal data](https://mlsanity.com/paper/2108.00866/) (2021)
- [A Deep Bayesian Nonparametric Framework for Robust Mutual Information Estimation](https://mlsanity.com/paper/2503.08902/) (2025)
- [Variational predictive resampling](https://mlsanity.com/paper/2605.11168/) (2026)

## Abstract (arXiv)

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, all models are misspecified, which brings into question the validity of the conventional Bayesian update. We present a scalable Bayesian nonparametric learning routine that enables posterior sampling through the optimization of suitably randomized objective functions. A Dirichlet process prior on the unknown data distribution accounts for model misspecification, and admits an embarrassingly parallel posterior bootstrap algorithm that generates independent and exact samples from the nonparametric posterior distribution. Our method is particularly adept at sampling from multimodal posterior distributions via a random restart mechanism. We demonstrate our method on Gaussian mixture model and sparse logistic regression examples.