---
res:
bibo_abstract:
- We use methods from combinatorics and algebraic statistics to study analogues
of birth-and-death processes that have as their state space a finite subset of
the m-dimensional lattice and for which the m matrices that record the transition
probabilities in each of the lattice directions commute pairwise. One reason such
processes are of interest is that the transition matrix is straightforward to
diagonalize, and hence it is easy to compute n step transition probabilities.
The set of commuting birth-and-death processes decomposes as a union of toric
varieties, with the main component being the closure of all processes whose nearest
neighbor transition probabilities are positive. We exhibit an explicit monomial
parametrization for this main component, and we explore the boundary components
using primary decomposition.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Steven
foaf_name: Evans, Steven N
foaf_surname: Evans
- foaf_Person:
foaf_givenName: Bernd
foaf_name: Sturmfels, Bernd
foaf_surname: Sturmfels
- foaf_Person:
foaf_givenName: Caroline
foaf_name: Caroline Uhler
foaf_surname: Uhler
foaf_workInfoHomepage: http://www.librecat.org/personId=49ADD78E-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-7008-0216
bibo_doi: 10.1214/09-AAP615
bibo_volume: 20
dct_date: 2010^xs_gYear
dct_publisher: Institute of Mathematical Statistics@
dct_title: Commuting birth and death processes@
...