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X-ray spectral analysis Parameter estimation Minimizer, stepping, local covariance MCMC or nested sampling –> Buchner+14 Stuck in local optima, non-gaussian optima, many parameters Combining multiple observations Stacking the data Hierarchical model –> Buchner+17a Average may not be meaningful Redshift blur Goodness of fit chi² test Visualize! Monte Carlo simulations Model comparison Invalid if at parameter border, model non-linear or not in the high-data regime (i.e., never valid) Model comparison Likelihood ratio, F-test Bayesian evidence or likelihood ratio, calibrate with Monte Carlo simulations –> Buchner+14 Invalid if at parameter border, model non-linear or not in the high-data regime (i.e., never valid)