@article{hollering_sullivant_2022, title={Exchangeable and sampling-consistent distributions on rooted binary trees}, ISSN={["1475-6072"]}, DOI={10.1017/jpr.2021.28}, abstractNote={Abstract We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling-consistent and exchangeable distributions on n-leaf phylogenetic trees is a polytope. We use this polytope to show that the set of all exchangeable and sampling-consistent distributions on four-leaf phylogenetic trees is exactly Aldous’ beta-splitting model, and give a description of some of the vertices for the polytope of distributions on five leaves. We also introduce a new semialgebraic set of exchangeable and sampling consistent models we call the multinomial model and use it to characterize the set of exchangeable and sampling-consistent distributions. Using this new model, we obtain a finite de Finetti-type theorem for rooted binary trees in the style of Diaconis’ theorem on finite exchangeable sequences.}, journal={JOURNAL OF APPLIED PROBABILITY}, author={Hollering, Benjamin and Sullivant, Seth}, year={2022}, month={Jan} }
 @article{hollering_sullivant_2021, title={Identifiability in phylogenetics using algebraic matroids}, volume={104}, ISSN={["1095-855X"]}, DOI={10.1016/j.jsc.2020.04.012}, abstractNote={Identifiability is a crucial property for a statistical model since distributions in the model uniquely determine the parameters that produce them. In phylogenetics, the identifiability of the tree parameter is of particular interest since it means that phylogenetic models can be used to infer evolutionary histories from data. In this paper we introduce a new computational strategy for proving the identifiability of discrete parameters in algebraic statistical models that uses algebraic matroids naturally associated to the models. We then use this algorithm to prove that the tree parameters are generically identifiable for 2-tree CFN and K3P mixtures. We also show that the k-cycle phylogenetic network parameter is identifiable under the K2P and K3P models.}, journal={JOURNAL OF SYMBOLIC COMPUTATION}, author={Hollering, Benjamin and Sullivant, Seth}, year={2021}, pages={142–158} }
 @article{harkonen_hollering_kashani_rodriguez_2020, title={Algebraic optimization degree}, volume={54}, ISSN={["1932-2240"]}, DOI={10.1145/3427218.3427222}, abstractNote={The Macaulay2 [5] package AlgebraicOptimization implements methods for determining the algebraic degree of an optimization problem. We describe the structure of an algebraic optimization problem and explain how the methods in this package may be used to determine the respective degrees. Special features include determining Euclidean distance degrees and maximum likelihood degrees. To our knowledge, this is the first comprehensive software package combining different methods in algebraic optimization. The package is available at https://github.com/Macaulay2/Workshop-2020-Cleveland/tree/ISSAC-AlgOpt/alg-stat/AlgebraicOptimization.}, number={2}, journal={ACM COMMUNICATIONS IN COMPUTER ALGEBRA}, author={Harkonen, Marc and Hollering, Benjamin and Kashani, Fatemeh Tarashi and Rodriguez, Jose Israel}, year={2020}, month={Jun}, pages={44–48} }