The biases caused by interpolated table models and their impact on X-ray spectroscopy

Abstract

Models for X-ray spectroscopy involving complex relativistic or plasma physics are commonly pre-computed on a grid, In this paper, we aim to quantify the potential biases and distortions introduced by the computational error and propagated into parameter inference by interpolating linearly these complex, non-linear models. We analyse the performance of Bayesian sampling algorithms on mock inference problems. Then, we model real observations of an accreting black hole X-ray binary in both the soft and hard states. We find that linear interpolation can a) greatly bias the posterior distribution of model parameters and b) distort the likelihood space to such a degree that posterior distributions become artificially multimodal. This multi-modality causes a noticeable loss in computational efficiency in both sampling and fitting techniques. As a result, exploring a given parameter space until convergence requires an extremely large computational cost. These findings call for improving the computational techniques used when fitting modern X-ray data, for example through better sampling algorithms and/or more sophisticated interpolation schemes