对数非中心χ 2分布的矩

Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

This paper is an extension of the work about the exponential increase of the power of two non-parametric tests: the $ Z $-test and the chi-square goodness-of-fit test. Subject to having auxiliary information, it is possible to improve exponentially relative to the size of the sample the power of the famous chi-square tests of independence and homogeneity. Improving the power of these statistical tests by using auxiliary information makes it possible either to reduce the probability of accepting the null hypothesis under the alternative hypothesis, or to reduce the size of the sample necessary …

基于卡方的MEDLINE引文分类评分函数

Chi-square-based scoring function for categorization of MEDLINE citations

目的：文本分类已被用于生物医学信息学中，用于识别包含相关主题的文档。我们开发了一种简单的方法，使用卡方评分函数来确定MEDLINE引文包含遗传相关主题的可能性。方法：我们的程序需要构建一个遗传和非遗传领域的文档语料库。我们使用MeSH描述符分配给MEDLINE引文进行分类任务。我们使用卡方检验比较了两个语料库中MeSH描述词的使用频率。如果MeSH描述符在遗传域语料库中的相对观察频率大于其在非遗传域语料库中的相对观察频率，则该描述符被认为是阳性指标。所提出的方法的输出是所有引文的分数列表，其中最高分数给予包含遗传领域典型的MeSH描述符的那些引文。结果：对一组734篇手动注释的MEDLINE引文进行了验证。它实现了预测准确率为0.87，召回率为0.69，精确率为0.64。我们通过将其与三种机器学习算法（支持向量机，决策树，朴素贝叶斯）进行比较来评估该方法。虽然差异在统计学上没有显著差异，但结果表明，我们的卡方评分与比较机器学习算法一样好。结论：我们认为卡方评分是一种有效的解决方案，以帮助分类MEDLINE引文。该算法在BITOLA基于文献的发现支持系统中实现，作为基因符号消歧过程的预处理器。

On the Existence of Uniformly Most Powerful Bayesian Tests With Application to Non-Central Chi-Squared Tests

Uniformly most powerful Bayesian tests (UMPBT's) are an objective class of Bayesian hypothesis tests that can be considered the Bayesian counterpart of classical uniformly most powerful tests. Because the rejection regions of UMPBT's can be matched to the rejection regions of classical uniformly most powerful tests (UMPTs), UMPBT's provide a mechanism for calibrating Bayesian evidence thresholds, Bayes factors, classical significance levels and p-values. The purpose of this article is to expand the application of UMPBT's outside the class of exponential family models. Specifically, we introduc…

火山图和正则化Chi统计量在遗传关联研究中的应用

Using Volcano Plots and Regularized-Chi Statistics in Genetic Association Studies

通常需要劳动密集型实验来从基因组中的疾病相关变体的列表中鉴定致病疾病变体。为了设计这样的实验，候选变体根据其与疾病的遗传关联的强度进行排名。然而，两种常用的遗传关联的测量，比值比（OR）和p值，可能以不同的顺序排列变异。为了将这两种方法整合到一个单一的分析中，我们将火山图方法从基因表达分析转移到遗传关联研究中。在原始设置中，火山图是倍数变化和t检验统计量（或p值的对数）的散点图，后者对样本大小更敏感。在遗传关联研究中，OR和Pearson卡方统计量（或其平方根，chi;或标准化log（OR））可以类似地用于火山图，允许它们的视觉检查。此外，这些图的几何解释导致了一种直观的方法，通过OR和卡方统计量的组合来过滤结果，我们称之为“正则化卡”。该方法通过火山图中的平滑曲线而不是对应于OR和卡方统计量的独立截止点的直角线来选择相关标记。正则化卡合并相对更多的信号，从变体具有较低的次要等位基因频率比卡方检验统计。由于罕见的变异往往具有更强的功能效应，正则化chi更适合于候选基因的优先级排序任务。

Asymptotic relatively more efficient test with auxiliary information: the case of the $Z$-test and the chi-square test

The main goal of this article is to study how an auxiliary information can be used to improve the efficiency of two famous statistical tests: the $ Z$-test and the chi-square test. Many definitions of auxiliary information can be found in the statistical literature. In this article, the notion of auxiliary information is discussed from a very general point of view and depends on the relevant test. These two statistical tests are modified so that this information is taken into account. It is shown in particular that the efficiency of these new tests is improved in the sense of Pitman's ARE. Som…

基于单元格可分离动态规划的二维列联表卡方族统计量的精确条件分布

Exact Conditional Distributions of Chi-Square-Family Statistics for Two-Way Contingency Tables, by Cell-Separable Dynamic Programming

该研究提出基于单元格可分离动态规划的方法，可计算二维列联表卡方族统计量的精确条件分布，为评估近似参照提供无蒙特卡洛的基准真值，适用于稀疏或异质表场景。