Priors are introduced into goodness‐of‐fit tests, both for unknown parameters in the tested distribution and on the alternative density. Neyman–Pearson theory leads to the test with the highest expected power. To make the test practical, we seek priors that make it likely a priori that the power will be larger than the level of the test but not too close to one. As a result, priors are sample size dependent. We explore this procedure in particular for priors that are defined via a Gaussian process approximation for the logarithm of the alternative density. In the case of testing for the uniform distribution, we show that the optimal test is of the U‐statistic type and establish limiting distributions for the optimal test statistic, both under the null hypothesis and averaged over the alternative hypotheses. The optimal test statistic is shown to be of the Cramér–von Mises type for specific choices of the Gaussian process involved. The methodology when parameters in the tested distribution are unknown is discussed and illustrated in the case of testing for the von Mises distribution. The Canadian Journal of Statistics 47: 560–579; 2019 © 2019 Statistical Society of Canada

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关于拟合优度检验中先验的使用

先验性被引入拟合优度测试中，既针对测试分布中的未知参数，也针对替代密度。内曼-皮尔逊理论以期望的最高功率引导测试。为了使测试切实可行，我们寻求先验方法，以使先验方法可以证明功效将大于测试水平，但又不能太接近测试水平。结果，先验与样本大小有关。我们特别针对先验探索这一过程，该先验是通过高斯过程近似法对替代密度的对数定义的。在测试均匀分布的情况下，我们表明最优测试是U统计类型并为最优检验统计建立极限分布，既可以在原假设下进行，也可以在替代假设下进行平均。对于涉及的高斯过程的特定选择，最佳测试统计数据显示为Cramér–von Mises类型。在测试冯·米塞斯分布的情况下，讨论并说明了当测试分布中的参数未知时的方法。《加拿大统计杂志》 47：560–579；2019©2019加拿大统计学会