Statistics for twenty-first century astrometry (2000 Heinrich K. Eichhorn Memorial Lecture)

H. K. Eichhorn had a lively interest in statistics during his entire scient ific career, and made a number of significant contributions to the statisti cal treatment of astrometric problems. In the past decade, a strong movemen t has taken place for the reintroduction of Bayesian methods of statistics into astronomy, driven by new understandings of the power of these methods as well as by the adoption of computationally-intensive simulation methods to the practical solution of Bayesian problems. In this paper I will discus s how Bayesian methods may be applied to the statistical discussion of astr ometric data, with special reference to several problems that were of inter est to Eichhorn.