Algebraic Methods in Statistics and Probability II
About this Title
Marlos A. G. Viana and Henry P. Wynn, Editors
This volume is based on lectures presented at the AMS Special Session on Algebraic Methods in Statistics and Probability—held March 27-29, 2009, at the University of Illinois at Urbana-Champaign—and on contributed articles solicited for this volume.
A decade after the publication of Contemporary Mathematics Vol. 287, the present volume demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models.
In statistics, this volume includes, among others, new results and applications in cubic regression models for mixture experiments, multidimensional Fourier regression experiments, polynomial characterizations of weakly invariant designs, toric and mixture models for the diagonal-effect in two-way contingency tables, topological methods for multivariate statistics, structural results for the Dirichlet distributions, inequalities for partial regression coefficients, graphical models for binary random variables, conditional independence and its relation to sub-determinants covariance matrices, connectivity of binary tables, kernel smoothing methods for partially ranked data, Fourier analysis over the dihedral groups, properties of square non-symmetric matrices, and Wishart distributions over symmetric cones.
In probability, this volume includes new results related to discrete-time semi Markov processes, weak convergence of convolution products in semigroups, Markov bases for directed random graph models, functional analysis in Hardy spaces, and the Hewitt-Savage zero-one law.
Graduate students and research mathematicians interested in applied mathematics, statistics, probability, and algebra.
Table of Contents
- Steen A. Andersson and Thomas Klein – Kiefer-complete classes of designs for cubic mixture models [MR 2730736]
- Vlad Stefan Barbu and Nikolaos Limnios – Some algebraic methods in semi-Markov chains [MR 2730737]
- Ronald A. Bates, Hugo Maruri-Aguilar, Eva Riccomagno, Rainer Schwabe and Henry P. Wynn – Self-avoiding generating sequences for Fourier lattice designs [MR 2730738]
- Frédéric Bertrand – Weakly invariant designs, rotatable designs and polynomial designs [MR 2730739]
- Cristiano Bocci, Enrico Carlini and Fabio Rapallo – Geometry of diagonal-effect models for contingency tables [MR 2730740]
- Peter Bubenik, Gunnar Carlsson, Peter T. Kim and Zhi-Ming Luo – Statistical topology via Morse theory persistence and nonparametric estimation [MR 2730741]
- Gregory Budzban and Göran Högnäs – Convolution products of probability measures on a compact semigroup with applications to random measures [MR 2730742]
- Santanu Chakraborty and Arunava Mukherjea – Completely simple semigroups of real $d\times d$ matrices and recurrent random walks [MR 2730743]
- Wan-Ying Chang, Rameshwar D. Gupta and Donald St. P. Richards – Structural properties of the generalized Dirichlet distributions [MR 2730744]
- Sanjay Chaudhuri and Gui Liu Tan – On qualitative comparison of partial regression coefficients for Gaussian graphical Markov models [MR 2730745]
- María Angélica Cueto, Jason Morton and Bernd Sturmfels – Geometry of the restricted Boltzmann machine [MR 2730746]
- Mathias Drton and Han Xiao – Smoothness of Gaussian conditional independence models [MR 2730747]
- Werner Ehm – Projections on invariant subspaces [MR 2730748]
- Steven N. Evans – A zero-one law for linear transformations of Lévy noise [MR 2730749]
- Hisayuki Hara and Akimichi Takemura – Connecting tables with zero-one entries by a subset of a Markov basis [MR 2730750]
- Kshitij Khare and Bala Rajaratnam – Covariance trees and Wishart distributions on cones [MR 2730751]
- Paul Kidwell and Guy Lebanon – A kernel smoothing approach to censored preference data [MR 2730752]
- M. Sofia Massa and Steffen L. Lauritzen – Combining statistical models [MR 2730753]
- Sonja Petrović, Alessandro Rinaldo and Stephen E. Fienberg – Algebraic statistics for a directed random graph model with reciprocation [MR 2730754]
- Giovanni Pistone and Maria Piera Rogantin – Regular fractions and indicator polynomials [MR 2730755]
- Marlos A. G. Viana – Dihedral Fourier analysis [MR 2730756]
- Tatjana von Rosen and Dietrich von Rosen – On a class of singular nonsymmetric matrices with nonnegative integer spectra [MR 2730757]
- A. Saeid Yasamin – Some hypothesis tests for Wishart models on symmetric cones [MR 2730758]