# Low-Budget Simulation-Based Inference with Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2408.15136 · HTML: https://mlsanity.com/paper/2408.15136/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 27 Aug 2024.

## Builds on (most cited first, 25 of 25)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [Bayesian Deep Ensembles via the Neural Tangent Kernel](https://mlsanity.com/paper/2007.05864/) (2020)
- [All You Need is a Good Functional Prior for Bayesian Deep Learning](https://mlsanity.com/paper/2011.12829/) (2020)
- [A Spectral Approach to Gradient Estimation for Implicit Distributions](https://mlsanity.com/paper/1806.02925/) (2018)
- [Tractable Function-Space Variational Inference in Bayesian Neural Networks](https://mlsanity.com/paper/2312.17199/) (2023)
- [Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation](https://mlsanity.com/paper/2208.13624/) (2022)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Galaxy Zoo: Probabilistic Morphology through Bayesian CNNs and Active Learning](https://mlsanity.com/paper/1905.07424/) (2019)
- [An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval](https://mlsanity.com/paper/1905.10659/) (2019)
- [Simulator-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problems](https://mlsanity.com/paper/2205.15680/) (2022)
- [Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference](https://mlsanity.com/paper/2310.04395/) (2023)
- [Robust Simulation-Based Inference in Cosmology with Bayesian Neural Networks](https://mlsanity.com/paper/2207.08435/) (2022)
- [Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability](https://mlsanity.com/paper/2310.13402/) (2023)
- [Balancing Simulation-based Inference for Conservative Posteriors](https://mlsanity.com/paper/2304.10978/) (2023)
- [Variational Inference with Coverage Guarantees in Simulation-Based Inference](https://mlsanity.com/paper/2305.14275/) (2023)
- [A point cloud approach to generative modeling for galaxy surveys at the field level](https://mlsanity.com/paper/2311.17141/) (2023)

## Built on by (most cited first, 5 of 5)

- [Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Models](https://mlsanity.com/paper/2504.17660/) (2025)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models](https://mlsanity.com/paper/2505.08683/) (2025)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)

## Abstract (arXiv)

Simulation-based inference methods have been shown to be inaccurate in the data-poor regime, when training simulations are limited or expensive. Under these circumstances, the inference network is particularly prone to overfitting, and using it without accounting for the computational uncertainty arising from the lack of identifiability of the network weights can lead to unreliable results. To address this issue, we propose using Bayesian neural networks in low-budget simulation-based inference, thereby explicitly accounting for the computational uncertainty of the posterior approximation. We design a family of Bayesian neural network priors that are tailored for inference and show that they lead to well-calibrated posteriors on tested benchmarks, even when as few as O(10) simulations are available. This opens up the possibility of performing reliable simulation-based inference using very expensive simulators, as we demonstrate on a problem from the field of cosmology where single simulations are computationally expensive. We show that Bayesian neural networks produce informative and well-calibrated posterior estimates with only a few hundred simulations.