# Neural Bayes estimation and selection for complex bivariate extremal dependence models

arXiv: https://arxiv.org/abs/2503.23156 · HTML: https://mlsanity.com/paper/2503.23156/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 65 references that are in the map.
- First posted on arXiv 29 Mar 2025.

## Builds on (most cited first, 28 of 28)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk](https://mlsanity.com/paper/2208.07590/) (2022)
- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Automatic Change-Point Detection in Time Series via Deep Learning](https://mlsanity.com/paper/2211.03860/) (2022)
- [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 graphical regression for jointly moderate and extreme Australian wildfires](https://mlsanity.com/paper/2308.14547/) (2023)
- [Fast parameter estimation of Generalized Extreme Value distribution using Neural Networks](https://mlsanity.com/paper/2305.04341/) (2023)
- [Pseudo-Marginal Hamiltonian Monte Carlo](https://mlsanity.com/paper/1607.02516/) (2016)
- [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)
- [Neural Bayes estimators for censored inference with peaks-over-threshold models](https://mlsanity.com/paper/2306.15642/) (2023)
- [Modelling across extremal dependence classes](https://mlsanity.com/paper/1408.5060/) (2014)
- [Deep Learning of Multivariate Extremes via a Geometric Representation](https://mlsanity.com/paper/2406.19936/) (2024)
- [Non-Stationary Dependence Structures for Spatial Extremes](https://mlsanity.com/paper/1411.3174/) (2014)
- [Asymmetric tail dependence modeling, with application to cryptocurrency market data](https://mlsanity.com/paper/1905.05056/) (2019)
- [Recognizing a Spatial Extreme dependence structure: A Deep Learning approach](https://mlsanity.com/paper/2103.10739/) (2021)
- [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)
- [Flexible space-time models for extreme data](https://mlsanity.com/paper/2411.19184/) (2024)
- [Flexible Modeling of Multivariate Spatial Extremes](https://mlsanity.com/paper/2206.11414/) (2022)
- [Joint modelling of the body and tail of bivariate data](https://mlsanity.com/paper/2209.05795/) (2022)
- [Modern extreme value statistics for Utopian extremes](https://mlsanity.com/paper/2311.11054/) (2023)

## Abstract (arXiv)

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for several models available in the multivariate extremes literature, particularly for the most flexible tail models, including those that interpolate between the two key dependence classes of `asymptotic dependence' and `asymptotic independence'. We focus on approaches that leverage neural networks to approximate Bayes estimators. In particular, we explore the properties of neural Bayes estimators for parameter inference for several flexible but computationally expensive models to fit, with a view to aiding their routine implementation. Owing to the absence of likelihood evaluation in the inference procedure, classical information criteria such as the Bayesian information criterion cannot be used to select the most appropriate model. Instead, we propose using neural networks as neural Bayes classifiers for model selection. Our goal is to provide a toolbox for simple, fast fitting and comparison of complex extreme-value dependence models, where the best model is selected for a given data set and its parameters subsequently estimated using neural Bayes estimation. We apply our classifiers and estimators to analyse the pairwise extremal behaviour of changes in horizontal geomagnetic field fluctuations at three different locations.