Reconstructing AGN X-ray spectral parameter distributions with Bayesian methods. I. Spectral analysis

X-ray spectra of active galactic nuclei (AGN) consist of several different emission and absorption components, which are often fitted manually with models chosen on a case-by-case basis. However, it becomes very hard for a survey with a large number of sources. In addition, when the signal-to-noise ratio (S/N) is low, there is a tendency to adopt an overly simplistic model, biasing the parameters and making their uncertainties unrealistic. We developed a Bayesian method for automatically fitting XMM-Newton AGN X-ray spectra with a consistent and physically motivated model including all spectral components, even when the data quality is low. An empirical model is used for the non-X-ray background. Noninformative priors were applied on the photon index (Gamma) and the hydrogen column density (N_H), while informative priors obtained from deep surveys were used to marginalize the remaining parameters. We tested this method using a realistically simulated sample of 5000 spectra reproducing typical population properties. Spectral parameters were randomly drawn from the priors, taking the luminosity function into account. Meaningful posterior probability density distributions were obtained for, for instance, N_H, Gamma, and L_X, even at low S/N, but in this case, we were unable to constrain the parameters of secondary components such as the reflection and soft excess. As a comparison, a maximum-likelihood approach with model selection among six models of different complexities was also applied to this sample. We find clear failures in the measurement of Gamma in most cases, and of N_H when the source is unabsorbed (N_H<10^22 cm-2). The results can hardly be used to reconstruct the parent distributions of the spectral parameters, while our Bayesian method provides meaningful multidimensional posteriors that will be used in a subsequent paper to infer the population. (abridged)