Author: Robert A. WijsmanPublisher: IMS
ISBN: 9780940600195
Category : Mathematics
Languages : en
Pages : 264
Book Description
Invariant Measures on Groups and Their Use in Statistics
Author: Robert A. WijsmanPublisher: IMS
ISBN: 9780940600195
Category : Mathematics
Languages : en
Pages : 264
Book Description
Invariant Measures on Groups and Their Use in Statistics
Author: Robert A. WijsmanPublisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 238
Book Description
This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.
Discrete Groups, Expanding Graphs and Invariant Measures
Author: Alex LubotzkyPublisher: Springer Science & Business Media
ISBN: 3034603320
Category : Mathematics
Languages : en
Pages : 201
Book Description
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.
Group Invariance Applications in Statistics
Author: Morris L. EatonPublisher: IMS
ISBN: 9780940600157
Category : Group theory
Languages : en
Pages : 148
Book Description
Algebraic Methods in Statistics and Probability
Author: Marlos A. G. VianaPublisher: American Mathematical Soc.
ISBN: 0821826875
Category : Mathematics
Languages : en
Pages : 354
Book Description
The 23 papers report recent developments in using the technique to help clarify the relationship between phenomena and data in a number of natural and social sciences. Among the topics are a coordinate-free approach to multivariate exponential families, some rank-based hypothesis tests for covariance structure and conditional independence, deconvolution density estimation on compact Lie groups, random walks on regular languages and algebraic systems of generating functions, and the extendibility of statistical models. There is no index. c. Book News Inc.
Discrete Groups, Expanding Graphs and Invariant Measures
Author: Alexander LubotzkyEpistemic Processes
Author: Inge S. HellandPublisher: Springer Nature
ISBN: 303081923X
Category : Mathematics
Languages : en
Pages : 251
Book Description
This book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes. The latter are processes, such as statistical investigations or quantum mechanical measurements, that can be used to obtain knowledge about something. Various topics in quantum theory are addressed, including the construction of a Hilbert space from reasonable assumptions and an interpretation of quantum states. Separate derivations of the Born formula and the one-dimensional Schrödinger equation are given. In concrete terms, a Hilbert space can be constructed under some technical assumptions associated with situations where there are two conceptual variables that can be seen as maximally accessible. Then to every accessible conceptual variable there corresponds an operator on this Hilbert space, and if the variables take a finite number of values, the eigenspaces/eigenvectors of these operators correspond to specific questions in nature together with sharp answers to these questions. This paves a new way to the foundations of quantum theory. The resulting interpretation of quantum mechanics is related to Hervé Zwirn's recent Convivial Solipsism, but it also has some relations to Quantum Bayesianism and to Rovelli's relational quantum mechanics. Niels Bohr's concept of complementarity plays an important role. Philosophical implications of this approach to quantum theory are discussed, including consequences for macroscopic settings. The book will benefit a broad readership, including physicists and statisticians interested in the foundations of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.
Stochastic Models, Information Theory, and Lie Groups, Volume 2
Author: Gregory S. ChirikjianPublisher: Springer Science & Business Media
ISBN: 0817649441
Category : Mathematics
Languages : en
Pages : 461
Book Description
This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.
Ordinal Invariant Measures for Individual and Group Changes in Ordered Categorical Data
Author: Encyclopaedia of Mathematics, Supplement III
Author: Michiel HazewinkelPublisher: Springer Science & Business Media
ISBN: 0306483734
Category : Mathematics
Languages : en
Pages : 564
Book Description
This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.