Algebraic Methods in Statistics and Probability II: AMS Special Session Algebraic Methods in Statistics and Probability, March 27-29, 2009, University of Illinois at Urbana-Champaign, Champaign, IL, Volume 2

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American Mathematical Soc., 2010 - Mathematics - 345 pages
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.
 

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Contents

Kiefercomplete Classes of Designs for Cubic Mixture Models
1
Some Algebraic Methods in SemiMarkov Chains
19
Selfavoiding Generating Sequences for Fourier Lattice Designs
37
Weakly Invariant Designs Rotatable Designs and Polynomial Designs
49
Geometry of Diagonaleffect Models for Contingency Tables
61
Statistical Topology via Morse Theory Persistence and Nonparametric Estimation
75
Convolution Products of Probability Measures on a Compact Semigroup with Applications to Random Measures
93
Completely Simple Semigroups of Real d d Matrices and Recurrent Random Walks
99
Projections on Invariant Subspaces
179
A Zeroone Law for Linear Transformations of LÚvy Noise
189
Connecting Tables with Zeroone Entries by a Subset of a Markov Basis
199
Covariance Trees and Wishart Distributions on Cones
215
A Kernel Smoothing Approach to Censored Preference Data
225
Combining Statistical Models
239
Algebraic Statistics for a Directed Random Graph Model with Reciprocation
261
Regular Fractions and Indicator Polynomials
285

Structural Properties of the Generalized Dirichlet Distributions
109
On Qualitative Comparison of Partial Regression Coefficients for Gaussian Graphical Markov Models
125
Geometry of the Restricted Boltzmann Machine
135
Smoothness of Gaussian Conditional Independence Models
155
Dihedral Fourier Analysis
305
On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra
319
Some Hypothesis Tests for Wishart Models On Symmetric Cones
327
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