an:06725171
Zbl 1373.62090
Rodriguez, Jose Israel; Tang, Xiaoxian
A probabilistic algorithm for computing data-discriminants of likelihood equations
EN
J. Symb. Comput. 83, 342-364 (2017).
0747-7171
2017
j
62F10 68W30 13P10 13P25
maximum likelihood estimation; likelihood equation; discriminant
Summary: An algebraic approach to the maximum likelihood estimation problem is to solve a very structured parameterized polynomial system called likelihood equations that have finitely many complex (real or non-real) solutions. The only solutions that are statistically meaningful are the real solutions with positive coordinates. In order to classify the parameters (data) according to the number of real/positive solutions, we study how to efficiently compute the discriminants, say data-discriminants (DD), of the likelihood equations. We develop a probabilistic algorithm with three different strategies for computing DDs. Our implemented probabilistic algorithm based on and is more efficient than our previous version [in: Proceedings of the 40th international symposium on symbolic and algebraic computation, ISSAC 2015, Bath, UK, July 6--9, 2015. New York, NY: Association for Computing Machinery (ACM). 307--314 (2015; Zbl 1345.65003)] and is also more efficient than the standard elimination for larger benchmarks. By applying RAGlib to a DD we compute, we give the real root classification of 3 by 3 symmetric matrix model.
1345.65003