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贝叶斯推断的必要性与接近贝叶斯形式的度量构造AI 解读

Many mathematical proofs of the necessity of Bayesian inference show, in effect, that betting procedures which have positive expected return for every value of an unknown parameter can be constructed to win money from non-Bayesian bookmakers. The yield of such betting procedures is here used as the basis for measures of the nearness to Bayesian form of the odds quoted by non-Bayesian bookmakers. Using one of these measures it is shown that the usual confidence intervals for…

摘要暂缺

保守统计推断AI 解读

Summary It is argued that statistical problems can usefully be divided into two classes: one-person problems for which Bayesian techniques are appropriate, and many-person problems, for which Bayesian techniques are not appropriate. Two conditions are presented which it is felt that statistical procedures for many-person problems should satisfy. Some of the consequences of these conditions are then investigated and discussed.

置信区间理论的若干反例AI 解读

Some families of distributions are presented for which certain Neyman confidence intervals have very poor conditional properties. In each case there is a 50% Neyman confidence interval I(x) for a parameter θ and a subset A of the sample space such that the conditional probability that I(X) covers θ given that X belongs to A is less than 0·2 for all θ and the conditional probability that I(X) covers θ given that X is not in A is at least 0·8 for all θ. The families of…

置信区间理论的若干反例AI 解读

Some families of distributions are presented for which certain Neyman confidence intervals have very poor conditional properties. In each case there is a 50% Neyman confidence interval I(x) for a parameter θ and a subset A of the sample space such that the conditional probability that I(X) covers θ given that X belongs to A is less than 0·2 for all θ and the conditional probability that I(X) covers θ given that X is not in A is at least 0·8 for all θ. The families of…