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.

翻译：无似然方法对于复杂依赖模型的推断具有吸引力，这要么是因为无法构建似然函数，要么是因为其计算成本极高。多元极值理论文献中的若干模型即属此类，特别是那些在“渐近依赖”与“渐近独立”这两个关键依赖类别之间进行插值的最灵活尾部模型。我们聚焦于利用神经网络逼近贝叶斯估计量的方法。具体而言，我们针对多个拟合计算成本高昂但灵活的模型，探究其参数推断中神经贝叶斯估计量的性质，以期推动这些模型的常规化应用。由于推断过程中不涉及似然函数计算，传统信息准则（如贝叶斯信息准则）无法用于选择最合适的模型。为此，我们提出将神经网络作为神经贝叶斯分类器用于模型选择。我们的目标是提供一个工具箱，用于简单、快速地拟合和比较复杂的极值依赖模型：首先为给定数据集选择最优模型，随后通过神经贝叶斯估计方法估计其参数。我们将所提出的分类器与估计量应用于分析三个不同地点水平地磁场波动变化的成对极值行为。