Scientific Reasoning: The Bayesian Approach
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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The Probability Calculus
The Laws of Probability
e The Duhem Problem
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argued argument assumption atomic weight Bayes's theorem Bayesian theory believe calculated Chapter claim classical statisticians clinical trial coin conditionalisation confidence interval confirmation consider consistent constraints credible interval criterion deductive defined density discussion epistemic epistemic probability equal equation error estimates evidence example experiment experimental fact fair betting quotients false Finetti finite Fisher given groups heads hence idea independent inductive inference interpretation intuitively Lakatos least squares likelihood linear regression logical mathematical mean measure method Neyman normal null hypothesis observed odds parameter particular patients percent Popper population possible posterior distribution posterior probability predictions Principle of Indifference prior distribution prior probability prob proba probabilistic probability axioms probability calculus probability function problem propositions Prout's hypothesis random sample random variables reason regarded rejected relative frequency relevant result scientific scientists sequence significance level significance tests standard deviation statistics stopping rule Suppose tion true Weisberg