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Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the real log-canonical thresholds (also known as stochastic complexities or learning coefficients) that quantify the large-sample behavior of the marginal likelihood in Bayesian inference. This provides the information needed for a recently introduced generalization of the Bayesian information criterion. Our mathematical developments treat the general setting of Laplace integrals whose phase functions are sums of squared differences between monomials and constants. We clarify how in this case real log-canonical thresholds can be computed using polyhedral geometry, and we show how to apply the general theory to the Laplace integrals associated with Gaussian latent tree and forest models. In simulations and a data example, we demonstrate how the mathematical knowledge can be applied in model selection.
We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that Gaussian l
Statistical models with latent structure have a history going back to the 1950s and have seen widespread use in the social sciences and, more recently, in computational biology and in machine learning. Here we study the basic latent class model propo
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This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many applicati
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