The Foundations of Statistics

act f apply B₁ basic acts behavior behavioralistic bilinear games bility called chapter coin concept conditional conditional probability consequences consider context convex convex sets Criterion decision problem defined definition denoted derived act discussion dominates elements equal equivalent event example Exercise expected value f and g Finetti finite number formal function Gamble hypothesis idea implies income infinite interpretation interval estimation least likelihood ratio likelihood-ratio test linear logic loss loss function lottery mathematical max L(f maximin minimax rule minimax theory mixed acts n-tuples notion null null hypothesis objectivistic views observation omelet particular partition problems personal probability personalistic view possible postulate preference proba probability measure qualitative probability random variables real numbers regarded seems sense sequence situation small world sufficient statistics Suppose sure-thing principle symmetry technical testing Theorem theory of personal tion typically utility verbalistic Wald