, Volume 36, Issue 1, pp 19-49

The Neyman-Pearson theory as decision theory, and as inference theory; with a criticism of the Lindley-savage argument for Bayesian theory

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The writer is grateful for helpful discussions of earlier versions of parts of this material with many colleagues, particularly D. V. Lindley, E. S. Pearson, J. Pratt, C. A. B. Smith, A. P. Dawid, G. Robinson, B. Norton, and M. Stone.