Title: Identifiability of Gaussian Structural Equation Models with Dependent Errors Having Equal Variances,
Abstract: In this paper, we prove that some Gaussian structural equation models with
dependent errors having equal variances are identifiable from their
corresponding Gaussian distributions. Specifically, we prove identifiability
for the Gaussian structural equation models that can be represented as
Andersson-Madigan-Perlman chain graphs (Andersson et al., 2001). These chain
graphs were originally developed to represent independence models. However,
they are also suitable for representing causal models with additive noise
(Peña, 2016. Our result implies then that these causal models can be
identified from observational data alone. Our result generalizes the result by
Peters and Bühlmann (2014), who considered independent errors having equal
variances. The suitability of the equal error variances assumption should be
assessed on a per domain basis.