定义概率树模型的方程
Equations defining probability tree models
摘要：
彩色概率树模型是对树图中描绘的事件之间的条件独立性进行编码的统计模型。它们比非常重要的一类特定于上下文的贝叶斯网络更一般。本文研究了他们的模型不变量理想的代数性质。这个理想的生成元可以很容易地从树图中读出，并且根据底层模型有一个简单的解释：它们是来自条件概率的优势比的差异。在这个分析中的一个关键发现是，树是一个方便的工具，用于理解精确的代数方式，其中参数空间上的和为1的条件转换为统计模型的联合概率上的和为1的条件。这使我们能够确定必要和充分的图形条件，分期树模型是一个复曲面品种的概率单纯形。
英文摘要：
Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class of context-specific Bayesian networks. In this paper, we study the algebraic properties of their ideal of model invariants. The generators of this ideal can be easily read from the tree graph and have a straightforward interpretation in terms of the underlying model: they are differences of odds ratios coming from conditional probabilities. One of the key findings in this analysis is that the tree is a convenient tool for understanding the exact algebraic way in which the sum-to-1 conditions on the parameter space translate into the sum-to-one conditions on the joint probabilities of the statistical model. This enables us to identify necessary and sufficient graphical conditions for a staged tree model to be a toric variety intersected with a probability simplex.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
