  We propose to use deep learning to estimate parameters in statistical models
when standard likelihood estimation methods are computationally infeasible. We
show how to estimate parameters from max-stable processes, where inference is
exceptionally challenging even with small datasets but simulation is
straightforward. We use data from model simulations as input and train deep
neural networks to learn statistical parameters. Our neural-network-based
method provides a competitive alternative to current approaches, as
demonstrated by considerable accuracy and computational time improvements. It
serves as a proof of concept for deep learning in statistical parameter
estimation and can be extended to other estimation problems.
