Semialgebraic Statistics And Latent Tree Models

Author: Piotr Zwiernik
Editor: CRC Press
ISBN: 1466576227
Size: 20,95 MB
Format: PDF
Read: 747

Semialgebraic Statistics and Latent Tree Models explains how to analyze statistical models with hidden (latent) variables. It takes a systematic, geometric approach to studying the semialgebraic structure of latent tree models. The first part of the book gives a general introduction to key concepts in algebraic statistics, focusing on methods that are helpful in the study of models with hidden variables. The author uses tensor geometry as a natural language to deal with multivariate probability distributions, develops new combinatorial tools to study models with hidden data, and describes the semialgebraic structure of statistical models. The second part illustrates important examples of tree models with hidden variables. The book discusses the underlying models and related combinatorial concepts of phylogenetic trees as well as the local and global geometry of latent tree models. It also extends previous results to Gaussian latent tree models. This book shows you how both combinatorics and algebraic geometry enable a better understanding of latent tree models. It contains many results on the geometry of the models, including a detailed analysis of identifiability and the defining polynomial constraints.

Algebraic Statistics

Author: Seth Sullivant
Editor: American Mathematical Soc.
ISBN: 1470435179
Size: 10,20 MB
Format: PDF
Read: 365

Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.

Handbook Of Graphical Models

Author: Marloes Maathuis
Editor: CRC Press
ISBN: 0429874243
Size: 13,76 MB
Format: PDF, Mobi
Read: 954

A graphical model is a statistical model that is represented by a graph. The factorization properties underlying graphical models facilitate tractable computation with multivariate distributions, making the models a valuable tool with a plethora of applications. Furthermore, directed graphical models allow intuitive causal interpretations and have become a cornerstone for causal inference. While there exist a number of excellent books on graphical models, the field has grown so much that individual authors can hardly cover its entire scope. Moreover, the field is interdisciplinary by nature. Through chapters by leading researchers from different areas, this handbook provides a broad and accessible overview of the state of the art. Key features: * Contributions by leading researchers from a range of disciplines * Structured in five parts, covering foundations, computational aspects, statistical inference, causal inference, and applications * Balanced coverage of concepts, theory, methods, examples, and applications * Chapters can be read mostly independently, while cross-references highlight connections The handbook is targeted at a wide audience, including graduate students, applied researchers, and experts in graphical models.

Probabilistic Foundations Of Statistical Network Analysis

Author: Harry Crane
Editor: CRC Press
ISBN: 1351807331
Size: 19,93 MB
Format: PDF, Docs
Read: 496

Probabilistic Foundations of Statistical Network Analysis presents a fresh and insightful perspective on the fundamental tenets and major challenges of modern network analysis. Its lucid exposition provides necessary background for understanding the essential ideas behind exchangeable and dynamic network models, network sampling, and network statistics such as sparsity and power law, all of which play a central role in contemporary data science and machine learning applications. The book rewards readers with a clear and intuitive understanding of the subtle interplay between basic principles of statistical inference, empirical properties of network data, and technical concepts from probability theory. Its mathematically rigorous, yet non-technical, exposition makes the book accessible to professional data scientists, statisticians, and computer scientists as well as practitioners and researchers in substantive fields. Newcomers and non-quantitative researchers will find its conceptual approach invaluable for developing intuition about technical ideas from statistics and probability, while experts and graduate students will find the book a handy reference for a wide range of new topics, including edge exchangeability, relative exchangeability, graphon and graphex models, and graph-valued Levy process and rewiring models for dynamic networks. The author’s incisive commentary supplements these core concepts, challenging the reader to push beyond the current limitations of this emerging discipline. With an approachable exposition and more than 50 open research problems and exercises with solutions, this book is ideal for advanced undergraduate and graduate students interested in modern network analysis, data science, machine learning, and statistics. Harry Crane is Associate Professor and Co-Director of the Graduate Program in Statistics and Biostatistics and an Associate Member of the Graduate Faculty in Philosophy at Rutgers University. Professor Crane’s research interests cover a range of mathematical and applied topics in network science, probability theory, statistical inference, and mathematical logic. In addition to his technical work on edge and relational exchangeability, relative exchangeability, and graph-valued Markov processes, Prof. Crane’s methods have been applied to domain-specific cybersecurity and counterterrorism problems at the Foreign Policy Research Institute and RAND’s Project AIR FORCE. ? ? ? ? ? ?

Nonparametric Models For Longitudinal Data

Author: Colin O. Wu
Editor: CRC Press
ISBN: 0429939086
Size: 17,31 MB
Format: PDF, Docs
Read: 915

Nonparametric Models for Longitudinal Data with Implementations in R presents a comprehensive summary of major advances in nonparametric models and smoothing methods with longitudinal data. It covers methods, theories, and applications that are particularly useful for biomedical studies in the era of big data and precision medicine. It also provides flexible tools to describe the temporal trends, covariate effects and correlation structures of repeated measurements in longitudinal data. This book is intended for graduate students in statistics, data scientists and statisticians in biomedical sciences and public health. As experts in this area, the authors present extensive materials that are balanced between theoretical and practical topics. The statistical applications in real-life examples lead into meaningful interpretations and inferences. Features: Provides an overview of parametric and semiparametric methods Shows smoothing methods for unstructured nonparametric models Covers structured nonparametric models with time-varying coefficients Discusses nonparametric shared-parameter and mixed-effects models Presents nonparametric models for conditional distributions and functionals Illustrates implementations using R software packages Includes datasets and code in the authors’ website Contains asymptotic results and theoretical derivations Both authors are mathematical statisticians at the National Institutes of Health (NIH) and have published extensively in statistical and biomedical journals. Colin O. Wu earned his Ph.D. in statistics from the University of California, Berkeley (1990), and is also Adjunct Professor at the Georgetown University School of Medicine. He served as Associate Editor for Biometrics and Statistics in Medicine, and reviewer for National Science Foundation, NIH, and the U.S. Department of Veterans Affairs. Xin Tian earned her Ph.D. in statistics from Rutgers, the State University of New Jersey (2003). She has served on various NIH committees and collaborated extensively with clinical researchers.

Collected Papers

Author: Emil Artin
Size: 18,64 MB
Format: PDF, Docs
Read: 932

Einf Hrung In Die Komplexe Analysis

Author: Wolfgang Fischer
Editor: Springer-Verlag
ISBN: 3834893773
Size: 16,25 MB
Format: PDF, ePub, Mobi
Read: 116

In den Bachelor-Studiengängen der Mathematik steht für die Komplexe Analysis (Funktionentheorie) oft nur eine einsemestrige 2-stündige Vorlesung zur Verfügung. Dieses Buch eignet sich als Grundlage für eine solche Vorlesung im 2. Studienjahr. Mit einer guten thematischen Auswahl, vielen Beispielen und ausführlichen Erläuterungen gibt dieses Buch eine Darstellung der Komplexen Analysis, die genau die Grundlagen und den wesentlichen Kernbestand dieses Gebietes enthält. Das Buch bietet über diese Grundausbildung hinaus weiteres Lehrmaterial als Ergänzung, sodass es auch für eine 3- oder 4 –stündige Vorlesung geeignet ist. Je nach Hörerkreis kann der Stoff unterschiedlich erweitert werden. So wurden für den „Bachelor Lehramt“ die geometrischen Aspekte der Komplexen Analysis besonders herausgearbeitet.

Der Harmonische Aufbau Der Welt

Author: Werner Diederich
Editor: Meiner Verlag
ISBN: 3787326804
Size: 17,56 MB
Format: PDF
Read: 287

Mit unbändiger Energie hat Johannes Kepler im frühen 17. Jahrhundert sein Projekt einer finalen Theorie des Himmels vorangetrieben. Werner Diederich zeigt in seinem verständlich geschriebenen und auch zur Einführung in Keplers Denken geeigneten Buch, dass dessen Ziel vor allem darin bestand, mit mathematischen Methoden die Harmonie im göttlichen Weltaufbau zu erfassen. - Das Bild, das wir uns von der Welt machen, ist mitgeprägt durch wissenschaftliche Erkenntnisse, die immer auch zeitbedingt sind. Das war vor 400 Jahren nicht anders, als der Mathematiker und Astronom Johannes Kepler ein Bild der Welt entwarf, das die damals neuesten astronomischen Hypothesen Nikolaus Kopernikus' sowie Tycho Brahes Beobachtungen des Himmels mit Spekulationen über eine allem zugrundeliegende Harmonik der Welt verband. Als bleibender Beitrag zur Astronomie wird heute vor allem Keplers Entdeckung der Ellipsengestalt der Planetenbahnen gesehen. Diese Sichtweise beruht jedoch auf der wissenschaftlichen Entwicklung der nachfolgenden Jahrhunderte, die einen ganz anderen Verlauf nahm, als Kepler es sich vorgestellt hatte. Diederich versucht in seinem äußerst klar und auch für Nicht-Mathematiker verständlich geschriebenen Buch Keplers Werk aus seiner Zeit und von seinem Selbstverständnis her zu begreifen. Für Kepler war seine Himmelsphysik Teil einer umfassenderen, letztlich theologischen Bemühung um die Erforschung der Gründe, aus denen Gott die Welt so geschaffen hat, wie wir sie vorfinden. Es ging ihm um nichts Geringeres als um das Aufspüren und mathematisch exakte Beschreiben himmlischer Harmonien - um die alte pythagoräische Vorstellung einer Sphärenmusik also. Keplers Hauptwerk ist demgemäß nicht, wie bisher zumeist angenommen, die 'Astronomia nova' (1609), sondern seine bislang weniger beachtete 'Weltharmonik' (Harmonice mundi, 1619).

Chemische Transportreaktionen

Author: Michael Binnewies
Editor: Walter de Gruyter
ISBN: 3110248964
Size: 18,67 MB
Format: PDF, ePub, Mobi
Read: 344

Unter dem Begriff Chemische Transportreaktionen fasst man eine Vielzahl von Reaktionen mit einem gemeinsamen Merkmal zusammen: Eine feste oder flA1/4ssige Komponente wird in Gegenwart eines gasfArmigen Reaktionspartners, des Transportmittels, verflA1/4chtigt und scheidet sich an anderer Stelle meist in Form gut ausgebildeter Kristalle wieder ab. Die Abscheidung kann dann erfolgen, wenn am Ort der Kristallisation andere AuAere Bedingungen herrschen als am Ort der VerflA1/4chtigung, in der Regel eine andere Temperatur. HAufig ist der Chemische Transport mit einem Reinigungseffekt verbunden. Wir haben es also mit einem Verfahren zur Herstellung reiner und gut kristallisierter Feststoffe zu tun. Insbesondere die Herstellung von Einkristallen stellt einen besonderen Wert dar, denn sie ermAglicht unter anderem die Bestimmung der Kristallstruktur mit Hilfe von RAntgenbeugungsverfahren. Aoeber diese Aspekte der reinen Grundlagenforschung hinaus haben Chemische Transportreaktionen auch eine praktische Bedeutung erlangt: Sie bilden die Grundlage der Funktionsweise von Halogenlampen. Auch ein groAtechnisches Verfahren beruht auf einer Chemischen Transportreaktion, das MOND-LANGER-Verfahren zur Herstellung von hochreinem Nickel.

Anorganische Chemie

Author: Erwin Riedel
Editor: Walter de Gruyter
ISBN: 3110225662
Size: 12,78 MB
Format: PDF, Kindle
Read: 309

"Riedel" - a student favorite - is now available in the revised 8th edition. The textbook addresses students with a major in chemistry and all who require a solid basic knowledge of inorganic chemistry. Clearly structured and focused on the essentials, the two parts of the book cover basic theory and inorganic material chemistry - within the framework of an excellent didactic concept. Contains419 color illustrations and106 tables."