Miracles and Statistics: The Casual Assumption of Independence

The primary theme of this address is cautionary: Statistical independence is far too often assumed casually, without serious concern for how common is dependence and how difficult it can be to achieve independence (or related structures).After initial discussion of statistics and religion, the address turns to miracles, especially Hume's critique and Babbage's reply.Stress is given the often tacit or unexamined assumption of independence among witnesses of a putative miracle.Other contexts of multiple testimony are treated, and the address ends with contemporary casual assumptions of independence: nuclear reactor safety, repeated measurements, and so forth.Other topics include prayer, circularity of argument, and the tension between skepticism about testimony and the pragmatic need to accept most of it provisionally.