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：神经点估计器是将数据映射到参数点估计的神经网络。此类估计器具有快速、无似然的特性，并且由于其摊销性质，适用于基于快速自举法的不确定性量化。本文旨在提高统计学家对这一相对新颖的推断工具的认识，并通过提供用户友好的开源软件促进其应用。我们同时关注从重复数据中进行推断这一普遍问题，并在神经框架下采用置换不变神经网络加以解决。通过广泛的仿真研究表明，这些神经点估计器能够以相对简便的方式快速且（在贝叶斯意义上）最优地估计弱识别和高参数化模型中的参数。我们通过红海极端海面温度分析展示了其应用价值：在训练完成后，我们能够在不到一秒的时间内从数百个空间场中获取参数估计及基于自举法的置信区间。