I will discuss some areas where statistical advances have been made in astronomical data analysis. The first area -- dubbed Concordance -- has been a subject of collaboration between astronomers and statisticians for seven years. The first Concordance paper was published in a statistics journal, the second was in a journal devoted to astronomy research, indicating the nature of the cross-disciplinary effort. Concordance is a framework for assessing systemat errors in the effective areas of telescopes that we have particularly applied to a group of X-ray instruments. The method was developed because X-ray telescopes are launched into orbit where they are no longer available for calibration using ground-based standards. The key statistical technique used in this project is multiplicative shrinkage with the first-ever use of priors on instrument effective areas combined in a Bayesian analysis. The project is the subject of further development that will be discussed. In X-ray polarimetry, one development involves the statistical handling of neural networks trained on simulated event tracks as the first step in data analysis.