Uncertainty Quantification in Astronomy

Despite the popularity of classical goodness fit tests such as Pearson's chi-squared and Kolmogorov-Smirnov, their applicability often faces serious challenges in practical applications. For instance, in a binned data regime, low counts may affect the validity of the asymptotic results. Excessively large bins, on the other hand, may lead to loss of power. In the unbinned data regime, tests such as Kolmogorov-Smirnov and Cramer-von Mises do not enjoy distribution-freeness if the models under study are multivariate and/or involve unknown parameters. As a result, one needs to simulate the distribution of the test statistic on a case-by-case basis. In this talk, I will discuss a testing strategy that allows us to overcome these shortcomings and equips experimentalists with a novel tool to perform goodness-of-fit while reducing substantially the computational costs. 

Large astronomical surveys of millions of sources such as eROSITA's
X-ray all-sky survey attempt to constrain the physical mechanisms at
play in distant galaxies. This talk will give an overview of some of the
statistical challenges in astrophysics, in particular uncertainty
estimation within and deciding between competing, physical, parametric
models. I will discuss which inference problems can be addressed with
machine learning and when astronomy is driven to custom Bayesian models
analysed with nested sampling or Hamiltonian Monte Carlo. Two highlights
from X-ray analysis include detection of significant variability in
Poisson data, and discovering accretion onto supermassive black holes
veiled in thick gas and dust.