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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)

- Elizabeth S Allman, John A Rhodes
- Mathematical biosciences
- 2003

A phylogenetic invariant for a model of biological sequence evolution along a phylogenetic tree is a polynomial that vanishes on the expected frequencies of base patterns at the terminal taxa. While the use of these invariants for phylogenetic inference has long been of interest, explicitly constructing such invariants has been problematic. We construct… (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)

- Elizabeth S Allman, James H Degnan, John A Rhodes
- Journal of mathematical biology
- 2011

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)

- Elizabeth S. Allman, John A. Rhodes
- Journal of Computational Biology
- 2006

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)

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)

- Elizabeth S Allman, James H Degnan, John A Rhodes
- Journal of theoretical biology
- 2011

One approach to estimating a species tree from a collection of gene trees is to first estimate probabilities of clades from the gene trees, and then to construct the species tree from the estimated clade probabilities. While a greedy consensus algorithm, which consecutively accepts the most probable clades compatible with previously accepted clades, can be… (More)

- Joseph P McCleery, Elizabeth Allman, Leslie J Carver, Karen R Dobkins
- Biological psychiatry
- 2007

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)

- Nicole A Tetreault, Atiya Y Hakeem, +4 authors John M Allman
- Journal of autism and developmental disorders
- 2012

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)

- Elizabeth S. Allman, James H. Degnan, John A. Rhodes
- Journal of Computational Biology
- 2013

The multispecies coalescent model describes the generation of gene trees from a rooted metric species tree and thus provides a framework for the inference of species trees from sampled gene trees. We prove that the STAR method of Liu et al. (2009) and generalizations of it, are statistically consistent methods of topological species tree inference under… (More)