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摘要翻译：
我们考虑了三水平因子分式阶乘设计的马尔可夫基。一旦我们有一个马尔可夫基，各种条件检验的$P$值是由马尔可夫链蒙特卡罗过程估计的。对于每次运行只有一个计数观测的设计实验，我们建立了一个广义线性模型，并考虑了一个对观测数据具有相同充分统计量的样本空间。每个模型都用协变量矩阵来表征，协变量矩阵是从我们打算测量的主要影响和相互作用影响中构造出来的。我们研究了具有$3^{p-q}$运行的分数阶乘设计，并注意到与$3^{p-q}$列联表的模型的对应性。
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英文标题：
《Markov basis for design of experiments with three-level factors》
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作者：
Satoshi Aoki and Akimichi Takemura
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最新提交年份：
2008
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
We consider Markov basis arising from fractional factorial designs with three-level factors. Once we have a Markov basis, $p$ values for various conditional tests are estimated by the Markov chain Monte Carlo procedure. For designed experiments with a single count observation for each run, we formulate a generalized linear model and consider a sample space with the same sufficient statistics to the observed data. Each model is characterized by a covariate matrix, which is constructed from the main and the interaction effects we intend to measure. We investigate fractional factorial designs with $3^{p-q}$ runs noting correspondences to the models for $3^{p-q}$ contingency tables.
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PDF链接：
https://arxiv.org/pdf/709.4323
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