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Unformatted text preview: 36 Chapter 3 Reverend Bayes and Professor Neyman Frank Porter April 18, 2010 Scientists use statistics in the process of gathering and interpreting infor mation relevant to interesting questions. They sometimes like to pretend that there is no philosophical issue; there is only one question and only one answer. There is an urge to “do it right”, or at least “do what works”, without much thought about what “it” is, or what they mean by “works”. However, these are crucial matters, and we lay the philosophical foundations in this chapter. We shall take it for granted that what the physicist does makes sense; that there is some “truth” that we are attempting to learn about via observations combined with logic, inference, and speculation. It is our goal to design a program of observations that reveals truth as eﬃciently (cheaply) as we can. This means that we try to make the most sensitive measurements and that we avoid false results. We take the point of view that there are three steps to learning about truth: the design, the observation, and the interpretation (omitting such “uninterest ing” steps as getting approved and building apparatus). The first step uses statistics to achieve eﬃciency and avoid false starts (bias). This is often done with simulation and use of control samples. The second step is the domain of “descriptive statistics”; we reduce the set of observations to simple statements that summarize the information content concerning the question of interest. The third step uses the description of the result, plus any other knowledge or beliefs, to arrive at an inference concerning a “truth”. It is in the latter two steps that considerable confusion arises. They are often comingled without due distinction. The role of statistics in the physical sciences may be contrasted with its role in some other fields. In particular, the notion of a “population” is often more virtual in the physical sciences than in some other fields. In physics, the sampling “population” may be an imagined repetition of an experiment many 37 38 CHAPTER 3. REVEREND BAYES AND PROFESSOR NEYMAN times, an infinite number in principle. This population doesn’t really exist, but we imagine what it would be like if it did. In some other fields, there is a real population being sampled, such as a population of people in a demographic study, or a population of widgets on a production line. The sampling population may be finite in size, and we typically try to learn about the whole population by sampling a fraction of it. Ultimately, the distinction is usually not so important, and the same methods can apply in both situations. But the virtual nature of the population we are interested in requires some faith in the words “in principle”....
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 Winter '09
 Physics, Statistics, Bayesian probability, prior distribution, Reverend Bayes

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