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Graphical Latent Structure Tests

Last modified: 2013-06-16

#### Abstract

Many models which include latent structure can be considered as semi-algebraic sets,and have recently begun to be studied from this perspective; this has shed much light on the dimension, identiability, and asymptotic statistical properties of these models. Though most of the attention has been on equality constraints, some progress has also been made on evaluating inequalities which might be used to test such models. However, the mathematical complexity of these approaches seems to have led to a gap between our theoretical understanding and the manner in which these models are applied in practice. In this paper we make a plea for some focus on nding simpler (in particular more graphical) and more computationally feasible ways to express such constraints, even at the cost of a loss of statistical power. Recent advances for directed acyclic graph models with latent variables and phylogenetic models are given as illustrations.

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