Simulation-Based Inference with Neural Posterior Estimation applied to X-ray spectral fitting: Demonstration of working principles down to the Poisson regime

Abstract

Neural networks are being extensively used for modelling data, especially in the case where no likelihood can be formulated. Although in the case of X-ray spectral fitting, the likelihood is known, we aim to investigate the neural networks ability to recover the model parameters but also their associated uncertainties, and compare its performance with standard X-ray spectral fitting, whether following a frequentist or Bayesian approach. We apply Simulation-Based Inference with Neural Posterior Estimation (SBI-NPE) to X-ray spectra. We train a network with simulated spectra, and then it learns the mapping between the simulated spectra and their parameters and returns the posterior distribution. The model parameters are sampled from a predefined prior distribution. To maximize the efficiency of the training of the neural network, yet limiting the size of the training sample to speed up the inference, we introduce a way to reduce the range of the priors, either through a classifier or a coarse and quick inference of one or multiple observations. SBI-NPE is demonstrated to work equally well as standard X-ray spectral fitting, both in the Gaussian and Poisson regimes, both on simulated and real data, yielding fully consistent results in terms of best fit parameters and posterior distributions. The inference time is comparable to or smaller than the one needed for Bayesian inference. On the other hand, once properly trained, an amortized SBI-NPE network generates the posterior distributions in no time. We show that SBI-NPE is less sensitive to local minima trapping than standard fit statistic minimization techniques. We find that the neural network can be trained equally well on dimension-reduced spectra, via a Principal Component Decomposition, leading to a shorter inference time. Neural posterior estimation thus adds up as a complementary tool for X-ray spectral fitting (abridged).