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While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability(More)
BACKGROUND A wealth of data has documented impairments in face processing in individuals with autism spectrum disorders (ASD). Recently, the suggestion has been made that these impairments may arise from abnormal development of a subcortical system involved in face processing that originates in the magnocellular pathway of the primate visual system. (More)
The general Markov model of the evolution of biological sequences along a tree leads to a parameterization of an algebraic variety. Understanding this variety and the polynomials, called phylogenetic invariants, which vanish on it, is a problem within the broader area of Algebraic Statistics. For an arbitrary trivalent tree, we determine the full ideal of(More)
For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter. We establish tree identifiability for a number of phylogenetic models, including a covarion model and a variety of(More)
While latent class models of various types arise in many statistical applications, it is often difficult to establish their identifiability. Focus-ing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability, utilizing algebraic(More)
We immunocytochemically identified microglia in fronto-insular (FI) and visual cortex (VC) in autopsy brains of well-phenotyped subjects with autism and matched controls, and stereologically quantified the microglial densities. Densities were determined blind to phenotype using an optical fractionator probe. In FI, individuals with autism had significantly(More)
Gene trees are evolutionary trees representing the ancestry of genes sampled from multiple populations. Species trees represent populations of individuals-each with many genes-splitting into new populations or species. The coalescent process, which models ancestry of gene copies within populations, is often used to model the probability distribution of gene(More)
Inference of evolutionary trees and rates from biological sequences is commonly performed using continuous-time Markov models of character change. The Markov process evolves along an unknown tree while observations arise only from the tips of the tree. Rate heterogeneity is present in most real data sets and is accounted for by the use of flexible mixture(More)
The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov process on a tree. For statistical use it is important to know if the model is identifiable; can both the tree topology(More)