Scientific Reasoning: The Bayesian ApproachThis book gives a clear comprehensive explanation and defense of the Bayesian account of scientific reasoning. It will be read not only by philosophers and theorists of scientific method but also by working scientists, uneasy about the justification of the statistical methods now in use. Since the book is designed to explain to the uninitiated the controversial theories it discusses, it can serve as an introduction to the role of statistics and probability in science. |
Contents
The Probability Calculus | 13 |
Two Different Interpretations of the Probability | 21 |
e Useful Theorems of the Calculus | 23 |
Copyright | |
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argument assigned assumption axioms Bayes's Theorem Bayesian approach Bayesian theory betting quotient Carnap Chapter characterised claim classical statisticians coin conclusion conditional probability confidence interval confirm consider credible interval defined degrees of belief discussion e₁ entails equal estimate evidence example experiment experimental fact false finite Fisher function given h₁ h₂ Hence hypoth independent inductive inductive reasoning inference intuitively Kendall and Stuart logical mean measure method Mises's theory Neyman Neyman-Pearson null hypothesis objective probabilities observations odds outcome space P(he parameter particular Popper possible posterior distribution posterior probability pothesis predictions Principle of Indifference prior distribution prior probability prob probabilistic probability calculus probability distribution Prout's hypothesis random variables reason refuted regarded rejected relative frequency result sample scientific scientists seems sentences sequence significance tests simply standard deviation statement statistical stopping rule subjective sufficient statistics Suppose tails tion tosses trial true X₁ zero