Neural Bayes estimation and selection of complex bivariate extremal dependence models.

Area of Science:

• Statistics
• Machine Learning
• Geophysics

Background:

• Complex dependence models in multivariate extremes often lack tractable likelihood functions.
• Flexible tail models, interpolating between asymptotic dependence and independence, are computationally expensive.
• Traditional information criteria (e.g., Bayesian Information Criterion) are inapplicable without likelihood evaluation.

Purpose of the Study:

• To develop and explore neural Bayes estimators for parameter inference in computationally demanding extreme value models.
• To introduce neural Bayes classifiers for model selection in likelihood-free settings.
• To provide a practical toolbox for efficient fitting and comparison of complex extreme-value dependence models.

Main Methods:

• Leveraging neural networks to approximate Bayes estimators for parameter inference.
• Employing neural networks as classifiers for model selection when likelihoods are unavailable.
• Applying developed methods to analyze geomagnetic field fluctuation data.

Main Results:

• Neural Bayes estimators demonstrate effectiveness for parameter inference in flexible extreme value models.
• Neural Bayes classifiers provide a viable alternative for model selection in likelihood-free scenarios.
• The methods were successfully applied to analyze pairwise extremal behavior in geomagnetic field data.

Conclusions:

• Neural network-based likelihood-free inference provides a powerful framework for complex dependence models.
• The proposed toolbox facilitates routine implementation and comparison of computationally intensive extreme value models.
• This approach aids in understanding extremal dependencies in geophysical phenomena.