# Neural Bayes estimators for censored inference with peaks-over-threshold models

arXiv: https://arxiv.org/abs/2306.15642 · HTML: https://mlsanity.com/paper/2306.15642/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 89 references that are in the map.
- First posted on arXiv 27 Jun 2023.

## Builds on (most cited first, 30 of 38)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks](https://mlsanity.com/paper/1802.06153/) (2018)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)
- [Fast covariance parameter estimation of spatial Gaussian process models using neural networks](https://mlsanity.com/paper/2012.15339/) (2020)
- [Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk](https://mlsanity.com/paper/2208.07590/) (2022)
- [Deep Integro-Difference Equation Models for Spatio-Temporal Forecasting](https://mlsanity.com/paper/1910.13524/) (2019)
- [Advances in Statistical Modeling of Spatial Extremes](https://mlsanity.com/paper/2007.00774/) (2020)
- [Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networks](https://mlsanity.com/paper/2208.07581/) (2022)
- [Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoods](https://mlsanity.com/paper/2305.04634/) (2023)
- [Deep Gaussian Covariance Network](https://mlsanity.com/paper/1710.06202/) (2017)
- [COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence](https://mlsanity.com/paper/2205.01224/) (2022)
- [Fast parameter estimation of Generalized Extreme Value distribution using Neural Networks](https://mlsanity.com/paper/2305.04341/) (2023)
- [Modeling spatial processes with unknown extremal dependence class](https://mlsanity.com/paper/1703.06031/) (2017)
- [Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process](https://mlsanity.com/paper/2208.03344/) (2022)
- [Modelling across extremal dependence classes](https://mlsanity.com/paper/1408.5060/) (2014)
- [Full likelihood inference for max-stable data](https://mlsanity.com/paper/1703.08665/) (2017)
- [Non-Stationary Dependence Structures for Spatial Extremes](https://mlsanity.com/paper/1411.3174/) (2014)
- [Modeling asymptotically independent spatial extremes based on Laplace random fields](https://mlsanity.com/paper/1507.02537/) (2015)
- [Higher-dimensional spatial extremes via single-site conditioning](https://mlsanity.com/paper/1912.06560/) (2019)
- [Recognizing a Spatial Extreme dependence structure: A Deep Learning approach](https://mlsanity.com/paper/2103.10739/) (2021)
- [Insights into the drivers and spatio-temporal trends of extreme Mediterranean wildfires with statistical deep-learning](https://mlsanity.com/paper/2212.01796/) (2022)
- [A Deep Learning Synthetic Likelihood Approximation of a Non-stationary Spatial Model for Extreme Streamflow Forecasting](https://mlsanity.com/paper/2212.07267/) (2022)
- [Likelihood estimators for multivariate extremes](https://mlsanity.com/paper/1411.3448/) (2014)
- [Bayesian inference for multivariate extreme value distributions](https://mlsanity.com/paper/1611.05602/) (2016)
- [Modelling Extremes of Spatial Aggregates of Precipitation using Conditional Methods](https://mlsanity.com/paper/2102.10906/) (2021)
- [Joint Estimation of Extreme Spatially Aggregated Precipitation at Different Scales through Mixture Modelling](https://mlsanity.com/paper/2111.08469/) (2021)

## Built on by (most cited first, 6 of 6)

- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Deep Generative Quantile Bayes](https://mlsanity.com/paper/2410.08378/) (2024)
- [Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks](https://mlsanity.com/paper/2505.03034/) (2025)
- [Neural Bayes estimation and selection for complex bivariate extremal dependence models](https://mlsanity.com/paper/2503.23156/) (2025)
- [Neural Architectures for Amortized Bayesian Inference: Statistical Foundations and Empirical Assessments](https://mlsanity.com/paper/2601.07944/) (2026)
- [Keeping Score: Adaptive, Tuning-Free Loss Weighting for Score-Augmented Neural Ratio Estimation](https://mlsanity.com/paper/2605.12118/) (2026)

## Abstract (arXiv)

Making inference with spatial extremal dependence models can be computationally burdensome since they involve intractable and/or censored likelihoods. Building on recent advances in likelihood-free inference with neural Bayes estimators, that is, neural networks that approximate Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models that use data augmentation techniques to encode censoring information in the neural network input. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference methods for spatial extremal dependence models. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators to make inference with popular extremal dependence models, such as max-stable, r-Pareto, and random scale mixture process models. We also illustrate that it is possible to train a single neural Bayes estimator for a general censoring level, precluding the need to retrain the network when the censoring level is changed. We illustrate the efficacy of our estimators by making fast inference on hundreds-of-thousands of high-dimensional spatial extremal dependence models to assess extreme particulate matter 2.5 microns or less in diameter (rm PM2.5) concentration over the whole of Saudi Arabia.