Abstract
After discussing some introductory concepts in statistical inference and contrasting these with our previous emphasis on exploratory data analysis, the basic axioms of probability are introduced, along with the additive and multiplication rules for computing probabilities of compound events. To aid in such computations, the counting rules for combinations and permutations are introduced. Bayes theorem is discussed, as are the various definitions of probability — classical, relative frequency and subjective — and it is emphasised that all definitions follow the same axioms and rules.
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Notes
That the basics of probability are typically explained using examples from games of chance (and we are no exception here) reflects the fact that the early concepts of probability theory were developed through the analysis of such parlour games. For example, if a pair of dice are rolled 12 times in succession, what should one bet on the chance of seeing at least one double six? How many rolls of the dice are required before the odds of seeing a double six is 50–50? Questions like these began to be asked around 1650 and attracted the attention of mathematicians such as Pascal and Fermat, who actually resolved the latter problem in what became the first theorem in probability. For more on the early history of probability, see Anders Hald, A History of Probability and Statistics and Their Applications before 1750 (Wiley, 2005).
See Mike Barrow, Statistics for Economics, Accounting and Business Studies, 6th edition (Prentice Hall, 2013), chapter 3, for a brief discussion of tree diagrams.
Bayes’ theorem, or ‘rule’ as it is of en referred to, has since become the foundation for a very influential school of statistical analysis, that of Bayesian inference, an approach that is rather too advanced to be covered in this text. Dale J. Poirier, Intermediate Statistics and Econometrics (MIT Press, 1995),
and Gary Koop, Bayesian Econometrics (Wiley, 2003), both provide introductory discussions of this very important approach to statistical modelling.
The story of Bayes’ theory through the last 250 years is recounted and popularised in Sharon Bertsch McGrayne, The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, & Emerged Triumphant from Two Centuries of Controversy (Yale University Press, 2011).
It is also a key technique for Nate Silver, The Signal and the Noise: The Art and Science of Prediction (Allen Lane, 2012).
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© 2014 Terence C. Mills
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Mills, T.C. (2014). Basic Concepts of Probability. In: Analysing Economic Data. Palgrave Texts in Econometrics. Palgrave Macmillan, London. https://doi.org/10.1057/9781137401908_7
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DOI: https://doi.org/10.1057/9781137401908_7
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