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268 DS perspective on statistical inferenceFrom the DS perspective, statistical prediction, estimation, and significancetesting depend on understanding and accepting the DS logical framework,as implemented through model-based computations that mix probabilisticand deterministic logic. They do not depend on frequentist propertiesof hypothetical (“imagined”) long runs of repeated application of any definedrepeatable statistical procedure, which properties are simply mathematicalstatements about the procedure. Knowledge of such long run properties mayguide choosing among statistical procedures, but drawing conclusions from aspecific application of a chosen procedure is something else again.Whereas the logical framework of DS inference has long been defined andstable, and presumably will not change, the choice of a model to be processedthrough the logic must be determined by a user or user community in eachspecific application. It has long been known that DS logic subsumes Bayesianlogic. A Bayesian instantiation of DS inference occurs automatically withinthe DS framework when a Bayesian model is adopted by a user. My argumentfor the importance of DS logic is not primarily that it encapsulatesBayes, however, but is that it makes available important classes of modelsand associated inferences that narrower Bayesian models are unable to represent.Specifically, it provides models where personal probabilities of “don’tknow” are appropriately introduced. In particular, Bayesian “priors” becomeoptional in many common statistical situations, especially when DS probabilitiesof “don’t know” are allowed. Extending Bayesian thinking in this waypromises greater realism in many or even most applied situations.24.2 Personal probabilityDS probabilities can be studied from a purely mathematical standpoint, butwhen they have a role in assessing uncertainties about specific real world unknowns,they are meant for interpretation as “personal” probabilities. To myknowledge, the term “personal” was first used in relation to mathematicalprobabilities by Émile Borel in a book (Borel, 1939), and then in statistics byJimmie Savage, as far back as 1950, and subsequently in many short contributionspreceding his untimely death in 1971. Savage was primarily concernedwith Bayesian decision theory, wherein proposed actions are based on posteriorexpectations. From a DS viewpoint, the presence of decision componentsis optional.The DS inference paradigm explicitly recognizes the role of a user in constructingand using formal models that represent his or her uncertainty. Noother role for the application of probabilities is recognized. Ordinary speechoften describes empirical variation as “random,” and statisticians often regardprobabilities as mathematical representations of “randomness,” whichthey are, except that in most if not all of statistical practice “random” varia-