Download e-book for iPad: Algebraic and Geometric Methods in Statistics by Paolo Gibilisco, Eva Riccomagno, Maria Piera Rogantin, Henry

By Paolo Gibilisco, Eva Riccomagno, Maria Piera Rogantin, Henry P. Wynn

This updated account of algebraic facts and knowledge geometry explores the rising connections among the 2 disciplines, demonstrating how they are often utilized in layout of experiments and the way they profit our realizing of statistical types, particularly, exponential versions. This e-book offers a brand new means of coming near near classical statistical difficulties and increases clinical questions that may by no means were thought of with out the interplay of those disciplines. starting with a short creation to every quarter, utilizing easy illustrative examples, the publication then proceeds with a set of stories and a few new effects written by way of top researchers of their respective fields. half III dwells in either classical and quantum details geometry, containing surveys of key effects and new fabric. ultimately, half IV offers examples of the interaction among algebraic records and knowledge geometry. desktop code and proofs also are to be had on-line, the place key examples are built in additional aspect.

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Subtracting this value from the expected dimension computed above, and taking into account the fact that all the points lie inside the simplex, we obtain r(d1 + d2 − 2) + r − 1 − r(d1 + d2 ) − r2 − 1 = r(r − 1). , of expected dimension) graphical model of conditional independence X1 and X2 given H, and the deficient dimension of the latent class model obtained by marginalising over the variable H. The study of higher-dimensional tables is still an open area of research. The mathematical machinery required to handle larger dimensions is considerably more complicated and relies on the notions of higher-dimensional tensors, rank tensors and non-negative rank tensors, for which only partial results exist.

Let H be an unobservable latent variable, defined on the set [r] = {1, . . , r}. In its most basic version, also known as the naive Bayes model, the LC model postulates that, conditional on H, the variables X1 , . . , Xk are mutually independent. Specifically, the joint distributions of X1 , . . ,i k ,h = p1 (i1 ) . . pk (ik )λh , (i1 , . . 1) (h) where λh is the marginal probability P r{H = h} and pl (il ) is the conditional marginal probability P r{Xl = il |H = h}, which we assume to be strictly positive for each h ∈ [r] and (i1 , .

2007). Performance of a new invariants method on homogeneous and nonhomogeneous quartet trees, Molecular Biology and Evolution 24(1), 288–93. ˇ Cencov, N. N. (1982). Statistical decision rules and optimal inference (Providence, RI, American Mathematical Society). Translation from the Russian edited by Lev J. Leifman. Consonni, G. and Pistone, G. (2007). Algebraic Bayesian analysis of contingency tables with possibly zero-probability cells, Statistica Sinica 17(4), 1355–70. Cover, T. M. and Thomas, J.

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