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配对比较实验的贝叶斯分析方法AI 解读

A Bayesian approach to the analysis of paired comparison experiments is presented. Two statistical models are considered: the multibinomial and the Bradley-Terry model. For each, the natural conjugate family of priors is used to represent prior beliefs, and the parameters of the prior are given meaningful interpretations. Two different estimators are suggested for the model parameters, the preference probabilities of the multibinomial model and the worth parameters of the…

成对比较实验的贝叶斯方法AI 解读

A Bayesian approach to the analysis of paired comparison experiments is presented. Two statistical models are considered: the multibinomial and the Bradley-Terry model. For each, the natural conjugate family of priors is used to represent prior beliefs, and the parameters of the prior are given meaningful interpretations. Two different estimators are suggested for the model parameters, the preference probabilities of the multibinomial model and the worth parameters of the…

尺度参数的 Λ-minimax 估计AI 解读

This note illustrates the application of the Λ-minimax principle (see, e.g., [6, Sect. 6.6]) to the estimation of a scale parameter. In particular, σ Λ-minimax estimator of the variance of a normal distribution is obtained when Λ is a subset of the class of natural conjugate prior distributions. Two cases considered are (1) the mean is known and (2) a fully specified prior distribution is available for the mean. Case 2 is reduced to Case 1.

多元位置参数的 Λ-minimax 估计AI 解读

The search for a linear Λ-minimax estimate (see, e.g., [19]) of a multivariate location parameter (with quadratic loss) is reduced to a problem of maximizing a continuous function on a compact, convex set—a problem which can be solved numerically with little difficulty. This reduction is accomplished by showing that a minimax theorem applies, thus changing a difficult minimax calculation to a simpler maximin problem. The technique is observed to be applicable to other,…

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关于序贯估计的一则札记AI 解读

Summary Moran (1951) infers that for some stationary stochastic processes, problems of parameter estimation may be simplified by employing sequential estimation procedures. He considers for example, estimation of the birth rate in the (stationary) Furry–Yule process. The purpose of this note is to indicate that Moran's suggestion may be useful for non-stationary processes as well. In particular, we consider maximum likelihood estimation of the parameter of a non-homogeneous,…