Statement – Seth Sullivant
نویسنده
چکیده
My research focus is on algebraic statistics and, in particular, on algebraic statistical models. These are statistical models that are described either parametrically or implicitly in terms of algebraic conditions on a natural parameter space. A precise definition appears in my paper with Drton [11]. I focus on algebraic statistical models because (a) they are ubiquitous in statistics, (b) the algebraic restriction means that they are generally well-behaved statistically, and (c) the underlying algebraic structure can be useful for making statistical inferences. From the mathematical standpoint, the algebraic structures that arise when analyzing algebraic statistical models lead to a range of challenging problems in algebraic geometry, commutative algebra, and combinatorics, and present many computational challenges. This research statement describes my past and present work on algebraic statistical models.
منابع مشابه
Research Statement – Seth Sullivant
I am broadly interested in developing and applying mathematical techniques which have traditionally been considered part of pure mathematics as tools of applied mathematics. Specifically, I work on problems in algebraic statistics, the research area concerned with applying techniques from algebraic geometry, commutative algebra, and combinatorics to address problems in parametric statistics and...
متن کاملToric Ideals in Algebraic Statistics Toric Ideals in Algebraic Statistics
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متن کاملA Gröbner Basis for the Secant Ideal of the Second Hypersimplex
We determine a Gröbner basis for the secant ideal of the toric ideal associated to the second hypersimplex ∆(2, n), with respect to any circular term order. The Gröbner basis of the secant ideal requires polynomials of odd degree up to n. This shows that the circular term order is 2-delightful, resolving a conjecture of Drton, Sturmfels, and the author. The proof uses Gröbner degenerations for ...
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