Algebraic Methods in Statistics and Probability II

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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Overview

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.

Read More Show Less

Product Details

  • ISBN-13: 9780821848913
  • Publisher: American Mathematical Society
  • Publication date: 6/18/2010
  • Series: Contemporary Mathematics Series , #516
  • Pages: 345
  • Product dimensions: 6.90 (w) x 10.00 (h) x 0.80 (d)

Table of Contents

Preface

Kiefer-complete Classes of Designs for Cubic Mixture Models Thomas Klein Klein, Thomas 1

Some Algebraic Methods in Semi-Markov Chains Nikolaos Limnios Limnios, Nikolaos 19

Self-avoiding Generating Sequences for Fourier Lattice Designs Henry P. Wynn Wynn, Henry P. 37

Weakly Invariant Designs, Rotatable Designs and Polynomial Designs Frederic Bertrand Bertrand, Frederic 49

Geometry of Diagonal-effect Models for Contingency Tables Fabio Rapallo Rapallo, Fabio 61

Statistical Topology via Morse Theory Persistence and Nonparametric Estimation Zhi-Ming Luo Luo, Zhi-Ming 75

Convolution Products of Probability Measures on a Compact Semigroup with Applications to Random Measures Goran Hognas Hognas, Goran 93

Completely Simple Semigroups of Real d x d Matrices and Recurrent Random Walks Arunava Mukherjea Mukherjea, Arunava 99

Structural Properties of the Generalized Dirichlet Distributions Donald St. P. Richards Richards, Donald St. P. 109

On Qualitative Comparison of Partial Regression Coefficients for Gaussian Graphical Markov Models Gui Liu Tan Gui, Liu Tan 125

Geometry of the Restricted Boltzmann Machine Bernd Sturmfels Sturmfels, Bernd 135

Smoothness of Gaussian Conditional Independence Models Han Xiao Han, Xiao 155

Projections on Invariant Subspaces Werner Ehm Ehm, Werner 179

A Zero-one Law for Linear Transformations of Levy Noise Steven N. Evans Evans, Steven N. 189

Connecting Tables with Zero-one Entries by a Subset of a Markov Basis Akimichi Takemura Takemura, Akimichi 199

Covariance Trees and Wishart Distributions on Cones Bala Rajaratnam Rajaratnam, Bala 215

A Kernel Smoothing Approach to Censored Preference Data Guy Lebanon Lebanon, Guy 225

Combining Statistical Models Steffen L. Lauritzen Lauritzen, Steffen L. 239

Algebraic Statistics for a Directed Random Graph Model with Reciprocation Stephen E. Fienberg Fienberg, Stephen E. 261

Regular Fractions and Indicator Polynomials Maria Piera Rogantin Rogantin, Maria Piera 285

Dihedral Fourier Analysis Marlos A. G. Viana Viana, Marlos A. G. 305

On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra Dietrich Von Rosen Von Rosen, Dietrich 319

Some Hypothesis Tests for Wishart Models On Symmetric Cones A. Saeid Yasamin Yasamin, A. Saeid 327

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