Neural point estimators are neural networks that map data to parameter point estimates. They are fast, likelihood free and, due to their amortised nature, amenable to fast bootstrap-based uncertainty quantification. In this paper, we aim to increase the awareness of statisticians to this relatively new inferential tool, and to facilitate its adoption by providing user-friendly open-source software. We also give attention to the ubiquitous problem of making inference from replicated data, which we address in the neural setting using permutation-invariant neural networks. Through extensive simulation studies we show that these neural point estimators can quickly and optimally (in a Bayes sense) estimate parameters in weakly-identified and highly-parameterised models with relative ease. We demonstrate their applicability through an analysis of extreme sea-surface temperature in the Red Sea where, after training, we obtain parameter estimates and bootstrap-based confidence intervals from hundreds of spatial fields in a fraction of a second.

翻译：神经点估计器是一种将数据映射到参数点估计的神经网络。这类方法具有快速、无需似然函数的特点，并且由于摊销性质，便于基于快速自助法的不确定性量化。本文旨在提升统计学家对这一相对新颖推断工具的认识，并通过提供用户友好的开源软件促进其应用。我们还关注从重复数据中进行推断这一普遍问题，在神经网络框架下利用置换不变神经网络加以解决。通过大量模拟研究表明，这些神经点估计器能够相对容易地快速且最优地（在贝叶斯意义上）估计弱辨识和高参数化模型中的参数。我们以红海极端海表温度分析为例展示其实用性——经过训练后，可在不到一秒内从数百个空间场中获得参数估计及基于自助法的置信区间。