**Contemporary Mathematics**

Volume: 516;
2010;
345 pp;
Softcover

MSC: Primary 20; 28; 42; 43; 60; 62;

Print ISBN: 978-0-8218-4891-3

Product Code: CONM/516

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

**Electronic ISBN: 978-0-8218-8195-8
Product Code: CONM/516.E**

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

# Algebraic Methods in Statistics and Probability II

Share this page *Edited by *
*Marlos A.G. Viana; Henry P. Wynn*

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.

#### Readership

Graduate students and research mathematicians interested in applied mathematics, statistics, probability, and algebra.

# Table of Contents

## Algebraic Methods in Statistics and Probability II

- Contents v6 free
- Preface vii8 free
- Kiefer-complete Classes of Designs for Cubic Mixture Models 110 free
- Some Algebraic Methods in Semi-Markov Chains 1928
- Self-avoiding Generating Sequences for Fourier Lattice Designs 3746
- Weakly Invariant Designs, Rotatable Designs and Polynomial Designs 4958
- Geometry of Diagonal-effect Models for Contingency Tables 6170
- Statistical Topology via Morse Theory Persistence and Nonparametric Estimation 7584
- Convolution Products of Probability Measures on a Compact Semigroup with Applications to Random Measures 93102
- Completely Simple Semigroups of Real d × d Matrices and Recurrent Random Walks 99108
- Structural Properties of the Generalized Dirichlet Distributions 109118
- On Qualitative Comparison of Partial Regression Coefficients for Gaussian Graphical Markov Models 125134
- Geometry of the Restricted Boltzmann Machine 135144
- Smoothness of Gaussian Conditional Independence Models 155164
- Projections on Invariant Subspaces 179188
- A Zero-one Law for Linear Transformations of Lévy Noise 189198
- Connecting Tables with Zero-one Entries by a Subset of a Markov Basis 199208
- Covariance Trees and Wishart Distributions on Cones 215224
- A Kernel Smoothing Approach to Censored Preference Data 225234
- Combining Statistical Models 239248
- Algebraic Statistics for a Directed Random Graph Model with Reciprocation 261270
- Regular Fractions and Indicator Polynomials 285294
- Dihedral Fourier Analysis 305314
- On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra 319328
- Some Hypothesis Tests for Wishart Models On Symmetric Cones 327336