This is a great book. Hacking describes the development of probability and statistics from the Renaissance to David Hume. His central questions are: What were Pascal, Huygens, Leibniz, Jacques Bernoulli, and all the others really doing? What problems were they trying to solve? What limitations were they working under? How did all this fit into other intellectual and mathematical problems of the day? How did all this affect the subsequent development of probability and statistics? Some of this clears up minor details that I had never grasped before, such as what was the problem with two dice that Pascal solved for the Chevalier de Mere. More important is the description of the intellectual implications of the development of modern probability and statistics. I had not known that the very name "probability" grew out of a profound religious and intellectual argument between the Jansenist Pascal and the Jesuits.
The book is full of historical gems. For example, the Dutch and English governments in the seventeenth century became infatuated with annuities as a way to finance theor expenses, especially wars. Most of the schemes were actuarially unsound. The early statisticians devoted a lot of energy to this problem and this led to major advances. Unfortunately the governments were not always pleased to be told they had no clothes. It all sounds terribly up to date.
In summary, this book covers material that is important not only in a histroical context but also for its relvance to many contemporary issues. It is well written and concise. If you want to know what the early probabilists were thinking about and how that affected the way we all think about uncertainty today, this is the book for you.
Traditionally, probability is identified with the long-run relative frequency of occurrence of an event, either in a sequence of repeated experiments or in an ensemble of "identically prepared" systems. We will refer to this view of probability as the "frequentist" view. It is the basis for the statistical procedures in use in the physical sciences.
Bayesian probability theory is founded on a much more general definition of probability. In BPT, probability is regarded as a real-number-valued measure of plausibility of a proposition when incomplete knowledge does not allow us to establish its truth or falsehood with certainty. The measure is taken on a scale where 1 represents certainty of the truth of the proposition, and 0 represents certainty of falsehood. This definition has an obvious connection with the colloquial use of the word "probability." In fact, Laplace viewed probability theory as simply "common sense reduced to calculation" (Laplace 1812, 1951). For Bayesians, then, probability theory is a kind of "quantitative epistemology," a numerical encoding of one's state of knowledge.
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