現代数学の系譜11 ガロア理論を読む17

現代数学の系譜11 ガロア理論を読む17at MATH

現代数学の系譜11 ガロア理論を読む17 - 暇つぶし2ch545:under frequentist inference, a hypothesis is typically tested without being assigned a probability. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses, i.e., the propositions whose truth or falsity is uncertain. Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies some prior probability, which is then updated in the light of new, relevant data (evidence). The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation. Objective and subjective Bayesian probabilities Broadly speaking, there are two views on Bayesian probability that interpret the 'probability' concept in different ways. For objectivists, probability objectively measures the plausibility of propositions, i.e. the probability of a proposition corresponds to a reasonable belief everyone (even a "robot") sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by requirements of rationality and consistency. For subjectivists, probability corresponds to a 'personal belief'.[2] For subjectivists, rationality and coherence constrain the probabilities a subject may have, but allow for substantial variation within those constraints. The objective and subjective variants of Bayesian probability differ mainly in their interpretation and construction of the prior probability.

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