标题： 测量关于随机参数的假设的支持度而无需估计其未知先验 显示英文标题

标题： Measuring support for a hypothesis about a random parameter without estimating its unknown prior

摘要： 对于参数随机性表示变异性而非不确定性的频率学派设定，一个假设相对于另一个假设的支持的理想度量是后验和先验对数几率之差。 对于先验分布无法被准确估计的情况，该理想支持可以由另一种支持度量代替，这种度量可以是对理想支持的任意预测器，并且在每次观察的基础上渐近无偏。 定义了两种合格的支持度量。 第一种是以总体为基准的最小最大最优，并且等价于特定的贝叶斯因子。 第二种是以最差样本为基准的最小最大最优，并且等价于归一化的最大似然。 它通过似然权重进行了扩展，以与更一般的模型兼容。 其中一个模型是两个独立正态样本的模型，这是基因表达微阵列数据分析的标准设定。 将该模型应用于蛋白质组学数据表明，从单一蛋白质的数据计算出的支持度可以非常接近使用20种蛋白质的数据所能获得的后验和先验对数几率之差的估计值。 这表明随机参数模型适用于其他参数分布无法可靠估计的情况。 显示英文摘要

摘要： For frequentist settings in which parameter randomness represents variability rather than uncertainty, the ideal measure of the support for one hypothesis over another is the difference in the posterior and prior log odds. For situations in which the prior distribution cannot be accurately estimated, that ideal support may be replaced by another measure of support, which may be any predictor of the ideal support that, on a per-observation basis, is asymptotically unbiased. Two qualifying measures of support are defined. The first is minimax optimal with respect to the population and is equivalent to a particular Bayes factor. The second is worst-sample minimax optimal and is equivalent to the normalized maximum likelihood. It has been extended by likelihood weights for compatibility with more general models. One such model is that of two independent normal samples, the standard setting for gene expression microarray data analysis. Applying that model to proteomics data indicates that support computed from data for a single protein can closely approximate the estimated difference in posterior and prior odds that would be available with the data for 20 proteins. This suggests the applicability of random-parameter models to other situations in which the parameter distribution cannot be reliably estimated.