Vol 8 No 1 (2017)
Aim and Scope:
Algebraic statistics focuses on mathematical aspects of statistical models, where algebraic, geometric and combinatorial insights can be useful to study behavior of statistical procedures. This approach has a long history in statistics and it can be traced back to Sir R.A. Fisher who used Abelian groups for experimental design and Karl Pearson who used polynomial algebra to study Gaussian mixture models. Since the turn of the century, the field has expanded and re-focused on applications of algebraic geometry, commutative algebra, and geometric combinatorics to the study of statistical models primarily for discrete data.
Recent advances in algebraic statistics have broadened the field beyond the 'traditional' algebraic statistics that focused on contingency tables and experimental design. The field is currently expanding in several directions. First, the study of Gaussian models have become an important part of algebraic statistics. Second, its computational aspects relying on numerical algebraic geometry are advancing to address statistical questions crucial for validity of statistical inference. Third, singular learning theory enables to study asymptotic statistics for models with hidden variables. Fourth, establishing identifiability of statistical models become an integral part of algebraic statistics. Finally, there is a strong focus on applications of these methods to phylogenetics, machine learning, biochemical reaction networks, social sciences, economics, and ecological inference.
The Journal of Algebraic Statistics seeks to publish new research articles in the braod area of algebraic statistics, both theoretical advnacements in the field - broadly defined - and its new applications. From time to time, review papers on an emerging topic will also be considered appropriate.