The Predictive Inference

A common type of inductive problem is to predict the nature of an unobserved finite sample of a given population on the basis of an observed finite sample of the same population. More precisely, given a class of events A , we examine a sample S n having n members, of which m i belong to the class B i . On the basis of our knowledge that m i / n of S n have been B i , we attempt to predict the ratio of members of B i to members of A in a sample S r containing r unobserved members of A. This type of inference has been called “predictive inference” by Carnap. It is not necessary to argue that all inductive problems reduce to this form; we merely observe that such problems frequently arise, and that they have practical and theoretical importance. In The Short Run I suggested that this kind of problem could be handled by first determining the long run probability P ( A, B i ) of B i , relative to A (presumably on the basis of the relative frequency F n ( A, B i ) of B i , to A in the observed sample S n ) and then predicting that the relative frequency of B i within the unobserved sample S r (the short run) will approximate P ( A, B i ) sufficiently for practical purposes. The foregoing procedure requires a rule of each of two types: a rule for the ascertainment of the values of long run probabilities, and a rule for the application of knowledge of long run probabilities to predictions in the short run. The Short Run was not concerned with the nature and justification of rules of the first type, but rather sought to justify a rule of the second type on the assumption that we already possess knowledge of long run probabilities

Basis (linear algebra) · Class (philosophy) · Econometrics · Inductive reasoning · Inference · Physics · Population · Sample (material) · Statistics · Type (biology) · Artificial Intelligence · Bayesian Methods and Mixture Models · Bayesian Modeling and Causal Inference · Computer Science · Demography · Mathematics · Statistical Methods and Bayesian Inference

• On Vindicating Induction

  Open Access•Wesley C Salmon•Philosophy of Science•1963

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• The philosophy of Hans Reichenbach

  Open Access•Wesley C Salmon•Synthese•1977

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