# Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applications

arXiv: https://arxiv.org/abs/2404.10899 · HTML: https://mlsanity.com/paper/2404.10899/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 16 Apr 2024.

## Builds on (most cited first, 19 of 19)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [Pareto Smoothed Importance Sampling](https://mlsanity.com/paper/1507.02646/) (2015)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [BayesFlow: Amortized Bayesian Workflows With Neural Networks](https://mlsanity.com/paper/2306.16015/) (2023)
- [Sequential Neural Posterior and Likelihood Approximation](https://mlsanity.com/paper/2102.06522/) (2021)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)
- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [Fast covariance parameter estimation of spatial Gaussian process models using neural networks](https://mlsanity.com/paper/2012.15339/) (2020)
- [Towards black-box parameter estimation](https://mlsanity.com/paper/2303.15041/) (2023)
- [A Gaussian-process approximation to a spatial SIR process using moment closures and emulators](https://mlsanity.com/paper/2208.03157/) (2022)

## Built on by (most cited first, 4 of 4)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [When the whole is greater than the sum of its parts: Scaling black-box inference to large data settings through divide-and-conquer](https://mlsanity.com/paper/2412.20323/) (2024)
- [Neural composite likelihood estimation: simulation based inference for time series](https://mlsanity.com/paper/2609.21762/) (2026)
- [Sample-Size Extrapolation in Simulation-Based Inference via Statistical Scaling](https://mlsanity.com/paper/2610.16820/) (2026)

## Abstract (arXiv)

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood function by leveraging the fact that data can be quickly simulated from the model, but converge slowly and/or poorly in high-dimensional settings. In this paper, we propose a framework for Bayesian posterior estimation by mapping data to posteriors of parameters using a neural network trained on data simulated from the complex model. Posterior distributions of model parameters are efficiently obtained by feeding observed data into the trained neural network. We show theoretically that our posteriors converge to the true posteriors in Kullback-Leibler divergence. Our approach yields computationally efficient and theoretically justified uncertainty quantification, which is lacking in existing simulation-based neural network approaches. Comprehensive simulation studies highlight our method's robustness and accuracy.