Resultants in genetic linkage analysis

Authors:
Ingileif B. Hallgrímsdóttir;Bernd Sturmfels
Affiliations:
Department of Statistics, University of California, Berkeley 94720, United States;Department of Mathematics, University of California, Berkeley 94720, United States
Venue:
Journal of Symbolic Computation
Year:
2006

Citing 2
Cited 0

Multihomogeneous resultant formulae by means of complexes

Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Algebraic geometry of Bayesian networks

Journal of Symbolic Computation

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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 algebraic invariants are presented as determinants of 32x32-matrices of linear forms in nine unknowns, a suitable format for computations with numerical data.