## Scientific reasoning: the Bayesian approach"Scientific Reasoning: The Bayesian Approach explains, in an accessible style, those elements of the probability calculus that are relevant to Bayesian methods, and argues that the probability calculus is best regarded as a species of logic." "Howson and Urbach contrast the Bayesian with the 'classical' view that was so influential in the last century, and demonstrate that familiar classical procedures for evaluating statistical hypotheses, such as significance tests, point estimation, confidence intervals, and other techniques, provide an utterly false basis for scientific inference. They also expose the well-known non-probabilistic philosophies of Popper, Lakatos, and Kuhn as similarly unscientific." "Scientific Reasoning shows how Bayesian theory, by contrast with these increasingly discredited approaches, provides a unified and highly satisfactory account of scientific method, an account which practicing scientists and all those interested in the sciences ought to master."--BOOK JACKET. |

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### Contents

The Probability Calculus | 17 |

Distributions and Densities | 37 |

The Classical and Logical Theories | 51 |

Copyright | |

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argued argument assigned assumption axioms Bayes's Theorem Bayesian approach Bayesian conditionalisation Bayesian theory betting Carnap Chapter claim classical statisticians clinical trial coin conditional probability confidence intervals confirm consider credible interval criterion defined degrees of belief density Dutch Book equal estimation evidence example experiment experimental fact factors false Fisher follows given Hence hypothe independent inductive inference interpretation intuitively Kendall and Stuart least squares linear logical mean measure method Neyman Neyman-Pearson normal null hypothesis objective probability observations odds outcome space parameter particular Popper population possible posterior distribution posterior probability predictions Principle of Indifference prior distribution prior probability probabili probabilistic probability axioms probability calculus probability distribution probability function Prout's hypothesis random sample random variables reason refuted regarded regression rejected relative frequency relevant result scientific scientists sentences sequence significance tests simply standard deviation statement statistical stopping rule subjective sufficient statistics Suppose tion tosses true