Semialgebraic Statistics And Latent Tree Models

Author: Piotr Zwiernik
Editor: CRC Press
ISBN: 1466576227
Size: 19,63 MB
Format: PDF, ePub
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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.

Probabilistic Foundations Of Statistical Network Analysis

Author: Harry Crane
Editor: CRC Press
ISBN: 1351807331
Size: 11,73 MB
Format: PDF, Kindle
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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: 12,60 MB
Format: PDF, Docs
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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.

Chain Event Graphs

Author: Rodrigo A. Collazo
Editor: CRC Press
ISBN: 1351646834
Size: 12,26 MB
Format: PDF, Docs
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?Written by some major contributors to the development of this class of graphical models, Chain Event Graphs introduces a viable and straightforward new tool for statistical inference, model selection and learning techniques. The book extends established technologies used in the study of discrete Bayesian Networks so that they apply in a much more general setting As the first book on Chain Event Graphs, this monograph is expected to become a landmark work on the use of event trees and coloured probability trees in statistics, and to lead to the increased use of such tree models to describe hypotheses about how events might unfold. Features: introduces a new and exciting discrete graphical model based on an event tree focusses on illustrating inferential techniques, making its methodology accessible to a very broad audience and, most importantly, to practitioners illustrated by a wide range of examples, encompassing important present and future applications includes exercises to test comprehension and can easily be used as a course book introduces relevant software packages Rodrigo A. Collazo is a methodological and computational statistician based at the Naval Systems Analysis Centre (CASNAV) in Rio de Janeiro, Brazil. Christiane Görgen is a mathematical statistician at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany. Jim Q. Smith is a professor of statistics at the University of Warwick, UK. He has published widely in the field of statistics, AI, and decision analysis and has written two other books, most recently Bayesian Decision Analysis: Principles and Practice (Cambridge University Press 2010).

Rising Road

Author: Sharon Davies
Editor: Oxford University Press
ISBN: 0199701903
Size: 19,91 MB
Format: PDF, Mobi
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It was among the most notorious criminal cases of its day. On August 11, 1921, in Birmingham, Alabama, a Methodist minister named Edwin Stephenson shot and killed a Catholic priest, James Coyle, in broad daylight and in front of numerous witnesses. The killer's motive? The priest had married Stephenson's eighteen-year-old daughter Ruth to Pedro Gussman, a Puerto Rican migrant and practicing Catholic. Sharon Davies's Rising Road resurrects the murder of Father Coyle and the trial of his killer. As Davies reveals with novelistic richness, Stephenson's crime laid bare the most potent bigotries of the age: a hatred not only of blacks, but of Catholics and "foreigners" as well. In one of the case's most unexpected turns, the minister hired future U.S. Supreme Court Justice Hugo Black to lead his defense. Though regarded later in life as a civil rights champion, in 1921 Black was just months away from donning the robes of the Ku Klux Klan, the secret order that financed Stephenson's defense. Entering a plea of temporary insanity, Black defended the minister on claims that the Catholics had robbed Ruth away from her true Protestant faith, and that her Puerto Rican husband was actually black. Placing the story in social and historical context, Davies brings this heinous crime and its aftermath back to life, in a brilliant and engrossing examination of the wages of prejudice and a trial that shook the nation at the height of Jim Crow. "Davies takes us deep into the dark heart of the Jim Crow South, where she uncovers a searing story of love, faith, bigotry and violence. Rising Road is a history so powerful, so compelling it stays with you long after you've finished its final page." --Kevin Boyle, author of the National Book Award-winning Arc of Justice "This gripping history...has all the makings of a Hollywood movie. Drama aside, Rising Road also happens to be a fine work of history." --History News Network

Handbook Of Graphical Models

Author: Mathias Drton
Editor: CRC Press
ISBN: 9781498788625
Size: 18,65 MB
Format: PDF, Kindle
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Graphical models are a statistical tool used for a wide range of applications. There has been a huge amount of research in this topic across statistics, mathematics and computer science in the last few decades, and the timing is right for a handbook that presents an overview of the state-of-the-art. This handbook presents a comprehensive overview of the area through a collection of 25-30 chapters from some of the leading researchers. Each chapter has been carefully edited to ensure that the handbook is consistent in style, level and notation, and that it is accessible for graduate students and researchers new to the topic. It is sure to become a landmark reference in the area.

Advances In Computational Intelligence

Author: Jing Liu
Editor: Springer
ISBN: 364230687X
Size: 14,74 MB
Format: PDF, Mobi
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This state-of-the-art survey offers a renewed and refreshing focus on the progress in evolutionary computation, in neural networks, and in fuzzy systems. The book presents the expertise and experiences of leading researchers spanning a diverse spectrum of computational intelligence in these areas. The result is a balanced contribution to the research area of computational intelligence that should serve the community not only as a survey and a reference, but also as an inspiration for the future advancement of the state of the art of the field. The 13 selected chapters originate from lectures and presentations given at the IEEE World Congress on Computational Intelligence, WCCI 2012, held in Brisbane, Australia, in June 2012.

The Geometry Of Remarkable Elements

Author: Constantin Mihalescu
Editor:
ISBN: 9780996874519
Size: 14,35 MB
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The book we are proposing here to the English-speaking reader is one that would have qualified at the beginning of the previous century as a book of "Modern Geometry" of the triangle and quadrilateral. Most of the results were obtained in the second half of the 19th century and the first half of the 20th century. The author was a retired artillery colonel and an enthusiastic amateur mathematician. This should come as no surprise, as for any artillery officer mathematics (and, especially, geometry) plays an important part in his formation. As the title surely suggests, this book is a rich collection of some of the most important properties of numerous points, lines, and circles related to triangles and quadrilaterals, as they were known by the mid-1950s. These include the nine-point circle, the Simson line, the orthopolar triangles, the orthopole, the Gergonne and Nagel points, the Miquel point and circle, the Carnot circle, the Brocard points, the Lemoine point and circles, the Newton-Gauss line, and many others. It was, probably, one of the most complete descriptions of the subject at the moment of the writing. The book was primarily addressed to young students but will be of interest to problem solvers in elementary geometry as well. Even geometers will find here new problems to inspire them.

Lectures On Algebraic Statistics

Author: Mathias Drton
Editor: Springer Science & Business Media
ISBN: 3764389052
Size: 13,45 MB
Format: PDF, Docs
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How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

Information Theory And Statistics

Author: Imre Csiszár
Editor: Now Publishers Inc
ISBN: 9781933019055
Size: 18,97 MB
Format: PDF, Kindle
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Information Theory and Statistics: A Tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory. The tutorial does not assume the reader has an in-depth knowledge of Information Theory or statistics. As such, Information Theory and Statistics: A Tutorial, is an excellent introductory text to this highly-important topic in mathematics, computer science and electrical engineering. It provides both students and researchers with an invaluable resource to quickly get up to speed in the field.