Probability Theory: The Logic of Science

analysis appears applications argument balls Bayes binomial calculation Chapter coin common sense conclusions consider Cox's theorems criterion data set decision theory defined density derivation equal equations error estimate evidence example expected fact finite Fisher frequency Gaussian give given Harold Jeffreys hypothesis improper prior independent induction inductive reasoning inference infinite sets integral intuitive Jeffreys knowledge Laplace Laplace's likelihood likelihood function limit loss function mathematical maximum entropy mean measure n₁ noise normal noted observed paradox physical plausible possible posterior distribution posterior pdf posterior probability predictions principle principle of indifference prior information prior probability probability assignment probability distribution probability theory problem product rule propositions random experiment reasoning relevant result robot rules of probability sampling distribution solution specified sufficient statistic suppose tell theorem theory as logic toss trials true widgets