Algebraic statistics

Algebraic statistics is the use of algebra to advance statistics. Algebra has been useful for experimental design, parameter estimation, and hypothesis testing.

Traditionally, algebraic statistics has been associated with the design of experiments and multivariate analysis (especially time series). In recent years, the term "algebraic statistics" has been sometimes restricted, sometimes being used to label the use of algebraic geometry and commutative algebra in statistics.

In the past, statisticians have used algebra to advance research in statistics. Some algebraic statistics led to the development of new topics in algebra and combinatorics, such as association schemes.

For example, Ronald A. Fisher, Henry B. Mann, and Rosemary A. Bailey applied Abelian groups to the design of experiments. Experimental designs were also studied with affine geometry over finite fields and then with the introduction of association schemes by R. C. Bose. Orthogonal arrays were introduced by C. R. Rao also for experimental designs.

Invariant measures on locally compact groups have long been used in statistical theory, particularly in multivariate analysis. Beurling's factorization theorem and much of the work on (abstract) harmonic analysis sought better understanding of the Wold decomposition of , which is important in time series statistics.

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