Scientific Reasoning (Howson, Urbach, 1989)

The Bayesian Approach

In this clearly reasoned defense of Bayes's Theorem — that probability can be used to reasonably justify scientific theories — Colin Howson and Peter Urbach examine the way in which scientists appeal to probability arguments, and demonstrate that the classical approach to statistical inference is full of flaws. Arguing the case for the Bayesian method with little more than basic algebra, the authors show that it avoids the difficulties of the classical system. The book also refutes the major criticisms leveled against Bayesian logic, especially that it is too subjective. This newly updated edition of this classic textbook is also suitable for college courses.

p.181 From the Bayesian viewpoint, therefore, estimation must be conducted with sufficient statistics.

p.182 A statistic t is defined to be an unbiased estimator of a parameter if its expectation is equal to the parameter's true value.

p.184 An estimator is said to be consistent when its probability distribution shows a diminishing scatter about the true value as the sample size increases.

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