  Sequential neural posterior estimation (SNPE) techniques have been recently
proposed for dealing with simulation-based models with intractable likelihoods.
Unlike approximate Bayesian computation, SNPE techniques learn the posterior
from sequential simulation using neural network-based conditional density
estimators by minimizing a specific loss function. The SNPE method proposed by
Lueckmann et al. (2017) used a calibration kernel to boost the sample weights
around the observed data, resulting in a concentrated loss function. However,
the use of calibration kernels may increase the variances of both the empirical
loss and its gradient, making the training inefficient. To improve the
stability of SNPE, this paper proposes to use an adaptive calibration kernel
and several variance reduction techniques. The proposed method greatly speeds
up the process of training, and provides a better approximation of the
posterior than the original SNPE method and some existing competitors as
confirmed by numerical experiments.
