CONTENTS 2.1 The Conflicts 11

2.1.1 Astronomy 11 2.2 Planetary Theory from Data Mining: Ptolemy, Copernicus, Kepler, Newton 12 2.3 Computation and Estimation: From Boscovitch to Legendre 13 2.4 From Philosophical Skepticism to Bayesian Inference: Hume, Bayes, and Price 15 2.5 Early Planet Hunting 17 2.6 Bayesian Statistics, Data Mining, and the Classical Tests of General Relativity 18 2.7 Statisticians Become Philosophers 22 2.8 The Digital Revolution 24 2.9 Statistics and Machine Learning Meet One Another 25 2.10 A Brief Reflection 26

2.1 THE CONFLICTS 2.1.1 Astronomy Our first and purest science, the mother of scientific methods, sustained by sheer curiosity, searching the heavens we cannot manipulate. From the beginning, astronomy has combined mathematical idealization, technological ingenuity, and indefatigable data collection with procedures to search through assembled data for the processes that govern the cosmos. Astronomers are, and ever have been, data miners, and for that reason astronomical methods (but not astronomical discoveries) have often been despised by statisticians and philosophers. Epithets laced the statistical literature: Ransacking! Data dredging! Double Counting! Statistical disdain was usually directed at social scientists and biologists, rarely if ever at astronomers, but the methodological attitudes and goals that many twentieth-century philosophers and statisticians rejected were creations of the astronomical tradition. The

philosophical criticisms were earlier and more direct. In the shadow (or in Alexander Pope’s phrasing, the light) cast on nature in the eighteenth century by the Newtonian triumph, David Hume revived arguments from the ancient Greeks to challenge the very possibility of coming to know what causes what. His conclusion was endorsed in the twentieth century by many philosophers who found talk of causation unnecessary or unacceptably metaphysical, and absorbed by many statisticians as a general suspicion of causal claims, except possibly when they are founded on experimental manipulation. And yet in the hands of a mathematician, Thomas Bayes, and another mathematician and philosopher, Richard Price, Hume’s essays prompted the development of a new kind of statistics, the kind we now call“Bayesian.”