Semialgebraic Statistics and Latent Tree Models

ISBN: 9780367377496 出版年：2015 页码：241 Zwiernik, Piotr CRC Press

Introduction A statistical model as a geometric object Algebraic statistics Toward semialgebraic statistics Latent tree models Structure of the book Semialgebraic statistics Algebraic and analytic geometry Basic concepts Real algebraic and analytic geometry Tensors and flattenings Classical examples Birational geometry Algebraic statistical models Discrete measures Exponential families and their mixtures Maximum likelihood of algebraic models Graphical models Tensors, moments, and combinatorics Posets and Mobius functions Cumulants and binary L-cumulants Tensors and discrete measures Submodularity and log-supermodularity Latent tree graphical models Phylogenetic trees and their models Trees Markov process on a tree The general Markov model Phylogenetic invariants The local geometry Tree cumulant parameterization Geometry of unidentified subspaces Examples, special trees, and submodels Higher number of states The global geometry Geometry of two-state models Full semialgebraic description Examples, special trees, and submodels Inequalities and estimation Gaussian latent tree models Gaussian models Gaussian tree models and Chow-Liu algorithm Gaussian latent tree models The tripod tree Bibliographical notes appear at the end of each chapter.