论文标题
通过允许负细胞计数连接表
Connecting Tables with Allowing Negative Cell Counts
论文作者
论文摘要
众所周知，计算离散loglinear模型的马尔可夫基础通常很难。因此，我们专注于通过马尔可夫的子集在光纤中连接表，在本文中，如果我们允许每个故事中的单元格计数为$ -1 $，则考虑连接表。在本文中，我们表明，如果马尔可夫基础的子集将包含所有表带有所有表的光纤中的所有表连接起来，则如果我们允许单元格计数为$ -1 $，则在该子集中连接光纤中移动。此外，我们表明，在某些情况下，在第三条交互模型下，我们可以通过所有基本动作（$ 2 \ times 2 \ times 2 $ 2 $ dinors）连接表，并允许$ x_ {ijk} \ geq -1 $。然后，我们将Markov Chain Monte Carlo（MCMC）计划应用于海军官员和入伍人口的经验数据。我们的计算实验表明它运行良好，我们以第三条交互模型的猜想结尾。
It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each tale to be $-1$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $-1$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables by all basic moves of $2 \times 2 \times 2$ minors with allowing $X_{ijk} \geq -1$. We then apply this Markov Chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model.
