Maximum likelihood estimation is a nonlinear optimization problem that arises in statistics.
One way to find a gobal optimal solution is to solve the critial equations.
This library contains methods to compute all complex solutions to these critical equations. It is an implementation in
Singular of the algorithms
described in Solving the Likelihood Equations.
This library contains methods to compute the independence varieties
and primary decomposition of Bayesian networks, as described in
Algebraic Geometry of Bayesian Networks.
The Macaulay2
version was written jointly with Michael Stillman.
The Singular
version will eventually be part of the contrib packages
in the standard release. This library is compatible with Singular version 3-0-1 or higher.
This library contains methods to compute the parametrization of the covariance matrix of a Gaussian graphical model. It has implementations of methods to compute the implicitization of this parametrization, to identify the parameters in the model and in particular to compute the Trek separation constraints described in the paper
Trek separation for Gaussian graphical models. Certain features of this library will only run on the operating system Mac OS X.
This program computes the first combinatorial
homotopy group of a simplical complex as described in
Foundations of a Connectivity Theory for Simplicial Complexes.
It is used to to analyze connectivity in social networks.
It is written in C++ and compiles under linux and unix.
This library contains an implementation of the
Gianni-Trager-Zacharias algorithm to compute the primary decomposition of a zero-dimensional ideal.
It is written for CoCoA IV. In the future, it will be extended to compute primary decomposition of general ideals in CoCoA V.