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总能实现良好的随机化序贯概率预测
Summary Building on the game theoretic framework for probability, we show that it is possible, using randomization, to make sequential probability forecasts that will pass any given battery of statistical tests. This result, an easy consequence of von Neumann's minimax theorem, simplifies and generalizes work by earlier researchers.
考虑二分子组选择的 P 值调整
Using a probability inequality, we show that if U = ([Udot], Ü), [Udot] = (U 1, …, U k), Ü = (U k + 1, …, U 2k ) has a multivariate normal distribution with mean vector zero and covariance matrices cov([Udot], [Udot]) = cov(Ü, Ü) = R, cov([Udot], Ü) = e'e – R, where R is a k × k correlation matrix and e = (1, …, 1), then P{|U 1| < c, …, |U 2k | < c} is minimized by setting all correlations in R equal to ½. This result is used to adjust the apparent significance of a…