On the Foundations of Statistical Inference I Binary Experiments

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On the Foundations of Statistical Inference I Binary Experiments
Allan Birnbaum
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= \0J is the set of such labels; in this context, each such probability experiment represents a (simple) statistical hypothesis H^. The problems of statistical inference treated by mathematical statistics are formulated on the basis of specified statistical experiments. (This includes problems of experimental design, which concern the appraisal and comparison of alternative statistical experimentso ) The character of objectivity which Is basic to modern proba- bility theory has two sources: Its... mathematical structure, based on unequivocal and consistent formal definitions of its terms, may be called mathematically objective « in contrast with some earlier versions of probability theory. When a probability experiment is used in relation to a physical phenomenon, with its methematical I. Vi- - ■- 'i ■ 29 elements linked (directly or indirectly) to physical entitles or events which are observable or verifiable (in fact or in principle), through xmequi vocal and consistent coordinating definitions, the resulting interpreted mathematical model may be called p hysica lly^ ob.

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