Resultants in Genetic Linkage Analysis
Quantitative Methods
2011-11-10 v2 Statistics Theory
Statistics Theory
Abstract
Statistical models for genetic linkage analysis of k-locus diseases are k-dimensional subvarieties of a (3^k-1)-dimensional probability simplex. We determine the algebraic invariants of these models with general characteristics for k=1, in particular we recover, and generalize, the Hardy-Weinberg curve. For k = 2, the invariants are presented as determinants of 32x32-matrices of linear forms in 9 unknowns, a suitable format for computations with numerical data.
Keywords
Cite
@article{arxiv.q-bio/0405001,
title = {Resultants in Genetic Linkage Analysis},
author = {Ingileif B. Hallgrimsdottir and Bernd Sturmfels},
journal= {arXiv preprint arXiv:q-bio/0405001},
year = {2011}
}
Comments
To appear in the Journal of Symbolic Computation, special issue on Computational Algebraic Statistics. 16 pages, 3 figures