By Paolo Gibilisco, Eva Riccomagno, Maria Piera Rogantin, Henry P. Wynn
This updated account of algebraic records and data 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 knowing of statistical types, particularly, exponential types. This ebook provides a brand new method of impending classical statistical difficulties and increases clinical questions that might by no means were thought of with no the interplay of those disciplines. starting with a quick creation to every quarter, utilizing easy illustrative examples, the publication then proceeds with a suite of reports and a few new effects written by means of major 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 data geometry. machine code and proofs also are on hand on-line, the place key examples are built in extra aspect.
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Extra resources for Algebraic and Geometric Methods in Statistics
We draw parallels between the statistical and geometric properties of latent class models and we illustrate geometrically the causes of many problems associated with maximum likelihood estimation and related statistical inference. In particular, we focus on issues of non-identiﬁability and determination of the model dimension, of maximisation of the likelihood function and on the eﬀect of symmetric data. We illustrate these phenomena with a variety of synthetic and real-life tables, of diﬀerent dimension and complexity.
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