The identifiability of tree topology for phylogenetic models, including covarion and mixture models

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 mixture models with a limited number of classes. The proof is based on the introduction of a more general model, allowing more states at internal nodes of the tree than at leaves, and the study of the algebraic variety formed by the joint distributions to which it gives rise. Tree identifiability is first established for this general model through the use of certain phylogenetic invariants.Comment: 20 pages, 1 figur

Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites

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 and the numerical parameters be determined from a joint distribution describing sequences only at the leaves of the tree? We establish that for generic parameters both the tree and all numerical parameter values can be recovered, up to clearly understood issues of `label swapping.' The method of analysis is algebraic, using phylogenetic invariants to study the variety defined by the model. Simple rational formulas, expressed in terms of determinantal ratios, are found for recovering numerical parameters describing the invariable sites

Black Indians, Zulus and Congos; Transformation and Transference of Community Traditions in New Orleans and Panama

This paper is a comparative study of three traditions that reflect the African diaspora: the Zulus of New Orleans, the black Indians of New Orleans and the Congo ritual of Panama. In all practices, the participant is transformed from citizen/worker/family member into an empowered being whose role is intricately connected to the reinforcement of cultural and community ties. In addition to presenting an overview of each tradition, I will discuss shared themes, parallel characterization, approaches to masking and comment on the interest of established practitioners to transfer their talents and histories to younger members of the community

Where Africa Meets Europe: Afro-Colonial Influences as Seen in The Tradition of The Mirrored Devils of Panama

The Republic of Panama is rich with folklore traditions which include as many different kinds of devils as there are provinces. Diablos sucios (dirty devils) and grandiablos (grand devils) can be seen in festivals across the country. Less visible are the diablos de espejo, or devils of the mirrors, which dance each year in the village of Escobal for the celebration of Corpus Christi. The dance movement performed throughout the day and the culminating drama which occurs in the local Catholic church at the end of day demonstrate a clear melding of African and Spanish colonial influences

Identifiability of parameters in latent structure models with many observed variables

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 utilizing algebraic arguments. A theorem of J. Kruskal for a simple latent-class model with finite state space lies at the core of our results, though we apply it to a diverse set of models. These include mixtures of both finite and nonparametric product distributions, hidden Markov models and random graph mixture models, and lead to a number of new results and improvements to old ones. In the parametric setting, this approach indicates that for such models, the classical definition of identifiability is typically too strong. Instead generic identifiability holds, which implies that the set of nonidentifiable parameters has measure zero, so that parameter inference is still meaningful. In particular, this sheds light on the properties of finite mixtures of Bernoulli products, which have been used for decades despite being known to have nonidentifiable parameters. In the nonparametric setting, we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed, but we explicitly describe the conditions.Comment: Published in at http://dx.doi.org/10.1214/09-AOS689 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org