Algebraic statistics applies concepts from algebraic geometry, commutative algebra, and geometric combinatorics to better understand the structure of statistical models, to improve statistical inference, and to explore new classes of models. Modern algebraic geometry was introduced to the field of statistics in the mid 1990s. Pistone and Wynn (1996) used Gröbner bases to address the issue of confounding in design of experiments, and Diaconis and Sturmfels (1998) used them to perform exact conditional tests. The term algebraic statistics was coined in the book by Pistone et al. (2001), which primarily addresses experimental design. The current algebraic statistics literature includes work on contingency tables, sampling methods, graphical and latent class models, and applications in areas such as statistical disclosure limitation (e.g., Dobra et al. (2009)), and computational biology and phylogenetics (e.g., Pachter and Sturmfels (2005)).
Algebraic Geometry of Statistical Models
Algebrai...
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Petrović, S., Slavković, A.B. (2011). Algebraic Statistics. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_112
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