  Because many of our X-ray telescopes are optimized towards observing faint
sources, observations of bright sources like X-ray binaries in outburst are
often affected by instrumental biases. These effects include dead time and
photon pile-up, which can dramatically change the statistical inference of
physical parameters from these observations. While dead time is difficult to
take into account in a statistically consistent manner, simulating dead
time-affected data is often straightforward. This structure makes the issue of
inferring physical properties from dead time-affected observations fall into a
class of problems common across many scientific disciplines. There is a growing
number of methods to address them under the names of Approximate Bayesian
Computation (ABC) or Simulation-Based Inference (SBI), aided by new
developments in density estimation and statistical machine learning. In this
paper, we introduce SBI as a principled way to infer variability properties
from dead time-affected light curves. We use Sequential Neural Posterior
Estimation to estimate the posterior probability for variability properties. We
show that this method can recover variability parameters on simulated data even
when dead time is variable, and present results of an application of this
approach to NuSTAR observations of the galactic black hole X-ray binary GRS
1915+105.
