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Chapter 2 Review of probability

Publisher
Elsevier Science & Technology
Identifiers
DOI: 10.1016/s0074-6142(06)80038-0
Disciplines
  • Computer Science
  • Earth Science
  • Mathematics

Abstract

Publisher Summary This chapter presents a brief review of the basic elements of probability. It is generally preferable to express uncertainty quantitatively, and this is done using numbers called probabilities. The chapter discusses the elements of probability that includes events, the sample space, and the axioms of probability. The axioms are the essential logical basis for the mathematics of probability—that is, the mathematical properties of probability can all be deduced from the axioms. However, the axioms are not informative about what probability actually means. There are two dominant views of the meaning of probability: the frequency view and the Bayesian (subjective) view. The frequency interpretation is intuitively reasonable and empirically sound. It is useful in such applications as estimating climatological probabilities by computing historical relative frequencies. The subjective interpretation is that probability represents the degree of belief, or quantified judgment, of a particular individual about the occurrence of an uncertain event. Two individuals can have different subjective probabilities for an event without either necessarily being wrong. This does not mean that an individual is free to choose any numbers and call them probabilities. The quantified judgment must be a consistent judgment. This means, among other things, that subjective probabilities must be consistent with the axioms of probability, and thus with the properties of probability implied by the axioms.

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