Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions
Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions
复制标题
通过多尺度引导程序测试三个区域的频率论和贝叶斯置信度
DOI：
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发表时间：
2008
影响因子：
1
通讯作者：
Hidetoshi Shimodaira
中科院分区：
文献类型：
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作者：
Hidetoshi Shimodaira
针对期望参数未知的多元正态模型，讨论了一种基于Bootstrap概率的频率p值和贝叶斯后验概率的计算方法。零假设被表示为参数向量的任意形状的区域。我们为自助概率的缩放律引入了新的函数形式，以便为单侧检验设计的多尺度自助方法也可以计算双侧检验的置信度，从而将适用性扩展到更广泛的假设类别。通过两步多尺度自助法和包含高阶项的方法，改进了标度律的参数估计。模型选择是重要的，不仅作为我们的方法的激励应用，而且作为方法中的一个重要组成部分。一个折衷的频率和贝叶斯之间的尝试表明，贝叶斯后验概率与noninformative先验被解释为一个频率的p值的“零侧”测试。
A new computation method of frequentist p values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is represented as an arbitrary-shaped region of the parameter vector. We introduce new functional forms for the scaling-law of bootstrap probability so that the multiscale bootstrap method, which was designed for a one-sided test, can also compute confidence measures of a two-sided test, extending applicability to a wider class of hypotheses. Parameter estimation for the scaling-law is improved by the two-step multiscale bootstrap and also by including higher order terms. Model selection is important not only as a motivating application of our method, but also as an essential ingredient in the method. A compromise between frequentist and Bayesian is attempted by showing that the Bayesian posterior probability with a noninformative prior is interpreted as a frequentist p value of “zero-sided” test.
DOI：
10.1073/pnas.93.14.7085
发表时间：
1996-07-09
影响因子：
11.1
作者：
Efron, B;Halloran, E;Holmes, S
通讯作者：
Holmes, S