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**Harvard**

Sadeghi, K. och Wermuth, N. (2016) *Pairwise Markov properties for regression graphs*.

** BibTeX **

@article{

Sadeghi2016,

author={Sadeghi, Kayvan and Wermuth, Nanny},

title={Pairwise Markov properties for regression graphs},

journal={STAT},

issn={2049-1573},

volume={5},

issue={1},

pages={286-294},

abstract={With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of conditional distributions, named regressions in joint responses. The involved random variables may be discrete, continuous or of both types. Such a generating process specifies for each response a conditioning set that contains just its regressor variables, and it leads to at least one valid ordering of all nodes in the corresponding regression graph that has three types of edge: one for undirected dependences among context variables, another for undirected dependences among joint responses and one for any directed dependence of a response on a regressor variable. For this regression graph, there are several definitions of pairwise Markov properties, where each interprets the conditional independence associated with a missing edge in the graph in a different way. We explain how these properties arise, prove their equivalence for compositional graphoids and point at the equivalence of each one of them to the global Markov property. Copyright (C) 2016 John Wiley & Sons, Ltd.},

year={2016},

keywords={seemingly unrelated regressions, mixed graphs, conditional-independence, models, likelihood},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 251387

A1 Sadeghi, Kayvan

A1 Wermuth, Nanny

T1 Pairwise Markov properties for regression graphs

YR 2016

JF STAT

SN 2049-1573

VO 5

IS 1

SP 286

OP 294

AB With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of conditional distributions, named regressions in joint responses. The involved random variables may be discrete, continuous or of both types. Such a generating process specifies for each response a conditioning set that contains just its regressor variables, and it leads to at least one valid ordering of all nodes in the corresponding regression graph that has three types of edge: one for undirected dependences among context variables, another for undirected dependences among joint responses and one for any directed dependence of a response on a regressor variable. For this regression graph, there are several definitions of pairwise Markov properties, where each interprets the conditional independence associated with a missing edge in the graph in a different way. We explain how these properties arise, prove their equivalence for compositional graphoids and point at the equivalence of each one of them to the global Markov property. Copyright (C) 2016 John Wiley & Sons, Ltd.

LA eng

DO 10.1002/sta4.122

LK http://dx.doi.org/10.1002/sta4.122

OL 30