Algebraic Methods in Statistics and Probability: AMS Special Session on Algebraic Methods and Statistics, April 8-9, 2000, University of Notre Dame, Notre Dame, Indiana

Algebraic methods and arguments in statistics and probability are well known, from Gauss' least squares principle through Fisher's method of variance decomposition. The relevance of group-theoretic arguments, for example, became evident in the 1980s. Such techniques continue to be of interest today, along with other developments, such as the use of graph theory in modelling complex stochastic systems.This volume is based on lectures presented at the AMS Special Session on Algebraic Methods and Statistics held at the University of Notre Dame (Indiana) and on contributed articles solicited for this volume. The articles are intended to foster communication between representatives of the diverse scientific areas in which these functions are utilized and to further the trend of utilizing algebraic methods in the areas of statistics and probability. This is one of few volumes devoted to the subject of algebraic methods in statistics and probability. The wide range of topics covered in this volume demonstrates the vigorous level of research and opportunities ongoing in these areas.

Table of Contents:
Simplicial inference by J. Aitchison A note on Nyman's equivalent formulation of the Riemann hypothesis by J.-F. Burnol On the construction of linear orthogonal arrays by extension by D. Collombier and A. Jourdan A coordinate-free approach to multivariate exponential families by A. Di Bucchianico and D. E. Loeb Best invariant predictive distributions by M. L. Eaton and W. D. Sudderth A family of probability densities related to the Riemann zeta function by W. Ehm Local field $U$-statistics by S. N. Evans Krawtchouk matrices from classical and quantum random walks by P. Feinsilver and J. Kocik Some rank-based hypothesis tests for covariance structure and conditional independence by Y. Gao and J. I. Marden Gaussian measures as limits on irreducible symmetric spaces and cones by P. Graczyk The covariance structure of the multivariate Liouville distributions by R. D. Gupta and D. St. Richards Reduction of regression models under symmetry by I. S. Helland Deconvolution density estimation on compact Lie groups by P. T. Kim and D. St. Richards On efficiency of indirect estimation of nonparametric regression functions by C. A. J. Klaassen, E.-J. Lee, and F. H. Ruymgaart Patterned matrices treated via linear spaces by T. Kollo and D. von Rosen Random walks on regular languages and algebraic systems of generating functions by S. P. Lalley The normal quasi-Wishart distribution by G. Letac and H. Massam Rank score statistics for spherical data by T. Neeman and T. Chang Graphical model search via essential graphs by M. D. Perlman Computational commutative algebra in discrete statistics by G. Pistone, E. Riccomagno, and H. P. Wynn Maximum covariance difference test for equality of two covariance matrices by A. Takemura and S. Kuriki The covariance structure of random permutation matrices by M. A. G. Viana The extendibility of statistical models by E. Wit and P. McCullagh.