Moment varieties from inverse Gaussian and gamma distributions

This repository contains auxiliary files for the manuscript Moment varieties from inverse Gaussian and gamma distributions by Oskar Henriksson, Lisa Seccia, and Teresa Yu.

Contents

The respository consists of the following directories:

• ranks containing Maple files rank_gamma.mpl and rank_inverse_gaussian.mpl for the rank computations discussed in §5.1 of the paper. These ranks prove that the $k$-th secant variety of $\mathcal{M}_d$ has the expected dimension for $k,d\leqslant 100$. Explicit choices of parameters and the resulting Jacobians are given in the files jacobians_gamma.txt and jacobians_inverse_gaussian.txt for the cases with $d\leq 8$, since these are used as the base case for the paper Moment varieties of the inverse Gaussian and gamma distributions are nondefective by Oskar Henriksson, Kristian Ranestad, Lisa Seccia, and Teresa Yu.

• identifiability_degrees containing Julia files gamma_identifiability_degree.jl and inverse_gaussian_identifiability_degree.jl for numerical estimation of the identifiability degrees, as well as a file certify_orbits.jl with a function for certifying orbits of a group action. Numerical certificates of the computed solutions are also included in the directory.

• ed_degrees containing Julia files edd_groebner.jl and edd_nag.jl for symbolic and numeric computation, respectively, of the ED degrees given in §5.3 of the paper.

Dependencies

The rank computations were done in Maple 2023. The rest of the code is written for Julia 1.10. For the numerical degree compuations, the Julia package HomotopyContinuation.jl v2.9.3 was used, whereas the symbolic degree computations were done using the Julia package Oscar v0.13.0 (see julia_environment/Manifest.toml for detailed Julia dependencies).