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Perfect Simulation

Author: Mark L. Huber
Publisher: CRC Press
ISBN: 1482232456
Size: 74.77 MB
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Exact sampling, specifically coupling from the past (CFTP), allows users to sample exactly from the stationary distribution of a Markov chain. During its nearly 20 years of existence, exact sampling has evolved into perfect simulation, which enables high-dimensional simulation from interacting distributions. Perfect Simulation illustrates the application of perfect simulation ideas and algorithms to a wide range of problems. The book is one of the first to bring together research on simulation from statistics, physics, finance, computer science, and other areas into a unified framework. You will discover the mechanisms behind creating perfect simulation algorithms for solving an array of problems. The author describes numerous protocol methodologies for designing algorithms for specific problems. He first examines the commonly used acceptance/rejection (AR) protocol for creating perfect simulation algorithms. He then covers other major protocols, including CFTP; the Fill, Machida, Murdoch, and Rosenthal (FMMR) method; the randomness recycler; retrospective sampling; and partially recursive AR, along with multiple variants of these protocols. The book also shows how perfect simulation methods have been successfully applied to a variety of problems, such as Markov random fields, permutations, stochastic differential equations, spatial point processes, Bayesian posteriors, combinatorial objects, and Markov processes.

Spatial Statistics And Computational Methods

Author: Jesper Møller
Publisher: Springer Science & Business Media
ISBN: 0387218114
Size: 78.30 MB
Format: PDF
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This volume shows how sophisticated spatial statistical and computational methods apply to a range of problems of increasing importance for applications in science and technology. It introduces topics of current interest in spatial and computational statistics, which should be accessible to postgraduate students as well as to experienced statistical researchers.

Markov Chain Monte Carlo

Author: W. S. Kendall
Publisher: World Scientific
ISBN: 9812564276
Size: 64.25 MB
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Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods. That variety stimulates new ideas and developments from many different places, and there is much to be gained from cross-fertilization. This book presents five expository essays by leaders in the field, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts. The essays derive from tutorial lectures at an interdisciplinary program at the Institute for Mathematical Sciences, Singapore, which exploited the exciting ways in which MCMC spreads across different disciplines.

Statistical Inference And Simulation For Spatial Point Processes

Author: Jesper Moller
Publisher: CRC Press
ISBN: 9780203496930
Size: 38.60 MB
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Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.

Probabilistic Foundations Of Statistical Network Analysis

Author: Harry Crane
Publisher: CRC Press
ISBN: 1351807331
Size: 14.91 MB
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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
Publisher: CRC Press
ISBN: 0429939086
Size: 79.71 MB
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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.

Measurement Error In Nonlinear Models

Author: Raymond J. Carroll
Publisher: CRC Press
ISBN: 9781420010138
Size: 16.35 MB
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It’s been over a decade since the first edition of Measurement Error in Nonlinear Models splashed onto the scene, and research in the field has certainly not cooled in the interim. In fact, quite the opposite has occurred. As a result, Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition has been revamped and extensively updated to offer the most comprehensive and up-to-date survey of measurement error models currently available. What’s new in the Second Edition? · Greatly expanded discussion and applications of Bayesian computation via Markov Chain Monte Carlo techniques · A new chapter on longitudinal data and mixed models · A thoroughly revised chapter on nonparametric regression and density estimation · A totally new chapter on semiparametric regression · Survival analysis expanded into its own separate chapter · Completely rewritten chapter on score functions · Many more examples and illustrative graphs · Unique data sets compiled and made available online In addition, the authors expanded the background material in Appendix A and integrated the technical material from chapter appendices into a new Appendix B for convenient navigation. Regardless of your field, if you’re looking for the most extensive discussion and review of measurement error models, then Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition is your ideal source.