1,051 research outputs found
Moment ideals of local Dirac mixtures
In this paper we study ideals arising from moments of local Dirac measures
and their mixtures. We provide generators for the case of first order local
Diracs and explain how to obtain the moment ideal of the Pareto distribution
from them. We then use elimination theory and Prony's method for parameter
estimation of finite mixtures. Our results are showcased with applications in
signal processing and statistics. We highlight the natural connections to
algebraic statistics, combinatorics and applications in analysis throughout the
paper.Comment: 26 pages, 3 figure
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
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