False confidence, non-additive beliefs, and valid statistical inference. (arXiv:1607.05051v2 [math.ST] UPDATED)

Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental questions about probability and inference that puzzled our founding fathers still exist and might even be more relevant today. To overcome these challenges, I propose to look beyond the two dominating schools of thought and ask what do scientists need out of statistics, do the existing frameworks meet these needs, and, if not, how to fill the void? To the first question, I contend that scientists seek to convert their data, posited statistical model, etc., into calibrated degrees of belief about quantities of interest. To the second question, I argue that any framework that returns additive beliefs, i.e., probabilities, necessarily suffers from false confidence---certain false hypotheses tend to be assigned high probability---and, therefore, risks making systematically misleading conclusions. This reveals the fundamental importance of non-additive beliefs in the context查看全文

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