Group items tagged

the rules of Bayesian statistics can be justified by requirements of rationality and consistency and interpreted as an extension of logic

According to the subjectivist view, probability quantifies a "personal belief".[3] Many modern machine learning methods are based on objectivist Bayesian principles

For objectivists, probability objectively measures the plausibility of propositions, i.e. the probability of a proposition corresponds to a reasonable belief everyone

or subjectivists, rationality and coherence constrain the probabilities a subject may have, but allow for substantial variation within those constraints.

"inverse probability" (because it infers backwards from observations to parameters, or from effects to causes)

"inverse probability" was largely supplanted by a collection of methods that came to be called frequentist statistics.[11]

In the objectivist stream, the statistical analysis depends on only the model assumed and the data analysed.[12] No subjective decisions need to be involved. In contrast, "subjectivist" statisticians deny the possibility of fully objective analysis for the general case.

frequentist statistics.

several arguments, such as the Cox axioms, the Dutch book argument, arguments based on decision theory and de Finetti's theorem.

Richard T. Cox showed that[6] Bayesian updating follows from several axioms, including two functional equations and a controversial hypothesis of differentiability.

A Dutch book is made when a clever gambler places a set of bets that guarantee a profit, no matter what the outcome of the bets. If a bookmaker follows the rules of the Bayesian calculus in the construction of his odds, a Dutch book cannot be made

every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.[19] Conversely, every Bayesian procedure is admissible.[20]

his work demonstrates that Bayesian-probability propositions can be falsified, and so meet an empirical criterion of Charles S. Peirce, whose work inspired Ramsey. (This falsifiability-criterion was popularized by Karl Popper.[25][26])