Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equations defining probability tree models   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.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat