Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on simulating parameters that sufficiently reproduce the observed data, and, at present, there is a lack of efficient methods to produce these simulations. We develop new black-box procedures to estimate parameters of statistical models based only on weak parameter structure assumptions. For well-structured likelihoods with frequent occurrences, such as in time series, this is achieved by pre-training a deep neural network on an extensive simulated database that covers a wide range of data sizes. For other types of complex dependencies, an iterative algorithm guides simulations to the correct parameter region in multiple rounds. These approaches can successfully estimate and quantify the uncertainty of parameters from non-Gaussian models with complex spatial and temporal dependencies. The success of our methods is a first step towards a fully flexible automatic black-box estimation framework.

翻译：深度学习算法近来已被证明是估计统计模型参数的有效工具，这些模型的模拟容易但似然计算困难。然而，这些方法的成功依赖于生成能够充分复现观测数据的模拟参数，而目前缺乏高效的方法来生成这些模拟。我们开发了新的黑盒程序，仅基于较弱的参数结构假设来估计统计模型的参数。对于结构良好且频繁出现的似然函数（如时间序列），我们通过在大规模模拟数据库上预训练深度神经网络来实现，该数据库涵盖广泛的数据规模。对于其他类型的复杂依赖性，迭代算法通过多轮模拟引导至正确的参数区域。这些方法能够成功估计并量化具有复杂时空依赖的非高斯模型参数的不确定性。我们方法的成功是迈向完全灵活的自适应黑盒估计框架的第一步。