Shiers, N.; Zwiernik, P.; Aston, J. A. D.; Smith, J. Q. The correlation space of Gaussian latent tree models and model selection without fitting. (English) Zbl 1506.62321 Biometrika 103, No. 3, 531-545 (2016). Summary: We provide a complete description of possible distributions consistent with any Gaussian latent tree model. This description consists of polynomial equations and inequalities involving covariances between the observed variables. Testing inequality constraints can be done using the inverse Wishart distribution and this leads to simple preliminary assessment of tree-compatibility. To test equality constraints we employ general techniques of tetrad analyses. This approach is effective even for small sample sizes and can be easily adjusted to test either entire models or just particular macrostructures of a tree. Our methods are simple to implement and do not require fitting of the model. The versatility of the techniques is illustrated by performing exploratory and confirmatory tetrad analyses in linguistic and biological settings respectively. Cited in 4 Documents MSC: 62H22 Probabilistic graphical models 62P10 Applications of statistics to biology and medical sciences; meta analysis Keywords:Gaussian distribution; latent tree model; tetrad analysis; tree constraint; tree quartet PDFBibTeX XMLCite \textit{N. Shiers} et al., Biometrika 103, No. 3, 531--545 (2016; Zbl 1506.62321) Full Text: DOI arXiv