This user-friendly, comprehensive course in probability and statistics as applied to physical and social science explains the probability calculus, distributions and densities, and the rivals of Beyesianism - the classical, logical, and subjective theories. Howson and Urbach clearly lay out the theory of classical inference, the Neyman-Pearson theory of significance tests, the classical theory of estimation, and regression analysis. The work is controversial, but gives a fair and accurate account of the anti-Bayesian views ...
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This user-friendly, comprehensive course in probability and statistics as applied to physical and social science explains the probability calculus, distributions and densities, and the rivals of Beyesianism - the classical, logical, and subjective theories. Howson and Urbach clearly lay out the theory of classical inference, the Neyman-Pearson theory of significance tests, the classical theory of estimation, and regression analysis. The work is controversial, but gives a fair and accurate account of the anti-Bayesian views it criticizes. The authors examined the way scientists actually appeal to probability arguments, and explain the 'classical' approach to statistical inference, which they demonstrate to be full of flaws. They then present the Bayesian method, showing that it avoids the difficulties of the classical system. Finally, they reply to all the major criticisms levelled against the Bayesian method, especially the charge that it is "too subjective".
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Applications of Bayesian statistics are just now elbowing their way into service in many fields, yet statistical education for users of statistics who are not professional statisticians is still mired in "orthodoxy." This somewhat older book is an excellent introduction to the field and explains the arguments and counter-arguments clearly and in a studied, logical fashion. There is a certain amount of polemic (par for the course), but polite in a British kind of way (nothing like the rough-and-tumble anti-frequentist zingers of ET Jaynes). The math is accessible to anyone who took algebra, and is present in just the right quantity.
