Symmetry Studies: An Introduction to the Analysis of Structured Data in Applications (Cambridge Series in Statistical and Probabilistic Mathematics)

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9780521841030: Symmetry Studies: An Introduction to the Analysis of Structured Data in Applications (Cambridge Series in Statistical and Probabilistic Mathematics)
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Experimental data can often be associated with or indexed by certain symmetrically interesting structures or sets of labels that appear, for example, in the study of short symbolic sequences in molecular biology, in preference or voting data, in (corneal) curvature data, and in studies of the handedness and entropy of symbolic sequences and elementary images. The symmetry studies introduced in this book describe the interplay among symmetry transformations that are characteristic of these sets of labels, their resulting classification, the algebraic decomposition of the data indexed by them, and the statistical analysis of the invariants induced by those decompositions. The overall purpose is to facilitate and guide the statistical study of the structured data from both a descriptive and inferential perspective. The text combines notions of algebra and statistics and develops a systematic methodology to better explore the many different data-analysis applications of symmetry.

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This book combines notions of algebra and statistics to develop a systematic methodology to better explore the interplay between symmetry-related research questions and their statistical inference. To guide the statistical study of structured data, the author examines the interplay between symmetry transformations that are applied to the sets of labels for the experimental data and the resulting data summaries that follow from those transformations.

Review:

"This is the perfect group theory book for students of statistics theory."
D.V. Feldman, Choice Magazine

"... useful for introducing these algebraic methods as tools in applied mathematics and statistics to relatively inexperienced students."
Seth Sullivant, Mathematical Reviews

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