Contemporary Mathematics 2001; 340 pp; softcover Volume: 287 ISBN10: 0821826875 ISBN13: 9780821826874 List Price: US$92 Member Price: US$73.60 Order Code: CONM/287
 Algebraic methods and arguments in statistics and probability are well known, from Gauss's least squares principle through Fisher's method of variance decomposition. The relevance of grouptheoretic 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. Readership Graduate students and research mathematicians interested in combinatorics, probability theory, stochastic processes, and statistics. Table of Contents  J. Aitchison  Simplicial inference
 J.F. Burnol  A note on Nyman's equivalent formulation of the Riemann hypothesis
 D. Collombier and A. Jourdan  On the construction of linear orthogonal arrays by extension
 A. Di Bucchianico and D. E. Loeb  A coordinatefree approach to multivariate exponential families
 M. L. Eaton and W. D. Sudderth  Best invariant predictive distributions
 W. Ehm  A family of probability densities related to the Riemann zeta function
 S. N. Evans  Local field \(U\)statistics
 P. Feinsilver and J. Kocik  Krawtchouk matrices from classical and quantum random walks
 Y. Gao and J. I. Marden  Some rankbased hypothesis tests for covariance structure and conditional independence
 P. Graczyk  Gaussian measures as limits on irreducible symmetric spaces and cones
 R. D. Gupta and D. St. Richards  The covariance structure of the multivariate Liouville distributions
 I. S. Helland  Reduction of regression models under symmetry
 P. T. Kim and D. St. Richards  Deconvolution density estimation on compact Lie groups
 C. A. J. Klaassen, E.J. Lee, and F. H. Ruymgaart  On efficiency of indirect estimation of nonparametric regression functions
 T. Kollo and D. von Rosen  Patterned matrices treated via linear spaces
 S. P. Lalley  Random walks on regular languages and algebraic systems of generating functions
 G. Letac and H. Massam  The normal quasiWishart distribution
 T. Neeman and T. Chang  Rank score statistics for spherical data
 M. D. Perlman  Graphical model search via essential graphs
 G. Pistone, E. Riccomagno, and H. P. Wynn  Computational commutative algebra in discrete statistics
 A. Takemura and S. Kuriki  Maximum covariance difference test for equality of two covariance matrices
 M. A. G. Viana  The covariance structure of random permutation matrices
 E. Wit and P. McCullagh  The extendibility of statistical models
