## 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 2This 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

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 Lévy 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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