Download or read book Dirichlet and Related Distributions written by Kai Wang Ng and published by John Wiley & Sons. This book was released on 2011-05-03 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response. The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inverted Dirichlet distribution, Dirichlet-multinomial distribution, the truncated Dirichlet distribution, the generalized Dirichlet distribution, Hyper-Dirichlet distribution, scaled Dirichlet distribution, mixed Dirichlet distribution, Liouville distribution, and the generalized Liouville distribution. Key Features: Presents many of the results and applications that are scattered throughout the literature in one single volume. Looks at the most recent results such as survival function and characteristic function for the uniform distributions over the hyper-plane and simplex; distribution for linear function of Dirichlet components; estimation via the expectation-maximization gradient algorithm and application; etc. Likelihood and Bayesian analyses of incomplete categorical data by using GDD, NDD, and the generalized Dirichlet distribution are illustrated in detail through the EM algorithm and data augmentation structure. Presents a systematic exposition of the Dirichlet-multinomial distribution for multinomial data with extra variation which cannot be handled by the multinomial distribution. S-plus/R codes are featured along with practical examples illustrating the methods. Practitioners and researchers working in areas such as medical science, biological science and social science will benefit from this book.

Download or read book Partitions Hypergeometric Systems and Dirichlet Processes in Statistics written by Shuhei Mano and published by Springer. This book was released on 2018-07-12 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on statistical inferences related to various combinatorial stochastic processes. Specifically, it discusses the intersection of three subjects that are generally studied independently of each other: partitions, hypergeometric systems, and Dirichlet processes. The Gibbs partition is a family of measures on integer partition, and several prior processes, such as the Dirichlet process, naturally appear in connection with infinite exchangeable Gibbs partitions. Examples include the distribution on a contingency table with fixed marginal sums and the conditional distribution of Gibbs partition given the length. The A-hypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from log-affine models. The normalizing constant is the A-hypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called A-hypergeometric system. The book presents inference methods based on the algebraic nature of the A-hypergeometric system, and introduces the holonomic gradient methods, which numerically solve holonomic systems without combinatorial enumeration, to compute the normalizing constant. Furher, it discusses Markov chain Monte Carlo and direct samplers from A-hypergeometric distribution, as well as the maximum likelihood estimation of the A-hypergeometric distribution of two-row matrix using properties of polytopes and information geometry. The topics discussed are simple problems, but the interdisciplinary approach of this book appeals to a wide audience with an interest in statistical inference on combinatorial stochastic processes, including statisticians who are developing statistical theories and methodologies, mathematicians wanting to discover applications of their theoretical results, and researchers working in various fields of data sciences.

Download or read book Theory and Use of the EM Algorithm written by Maya R. Gupta and published by Now Publishers Inc. This book was released on 2011 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the expectation-maximization (EM) algorithm and provides an intuitive and mathematically rigorous understanding of this method. Theory and Use of the EM Algorithm is designed to be useful to both the EM novice and the experienced EM user looking to better understand the method and its use.

Download or read book Mixture Models and Applications written by Nizar Bouguila and published by Springer. This book was released on 2019-08-13 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on recent advances, approaches, theories and applications related to mixture models. In particular, it presents recent unsupervised and semi-supervised frameworks that consider mixture models as their main tool. The chapters considers mixture models involving several interesting and challenging problems such as parameters estimation, model selection, feature selection, etc. The goal of this book is to summarize the recent advances and modern approaches related to these problems. Each contributor presents novel research, a practical study, or novel applications based on mixture models, or a survey of the literature. Reports advances on classic problems in mixture modeling such as parameter estimation, model selection, and feature selection; Present theoretical and practical developments in mixture-based modeling and their importance in different applications; Discusses perspectives and challenging future works related to mixture modeling.

Download or read book Probability Distributions Used in Reliability Engineering written by Andrew N O'Connor and published by RIAC. This book was released on 2011 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.

Download or read book Continuous Multivariate Distributions Volume 1 written by Samuel Kotz and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.

Download or read book Principles and Methods for Data Science written by and published by Elsevier. This book was released on 2020-05-28 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principles and Methods for Data Science, Volume 43 in the Handbook of Statistics series, highlights new advances in the field, with this updated volume presenting interesting and timely topics, including Competing risks, aims and methods, Data analysis and mining of microbial community dynamics, Support Vector Machines, a robust prediction method with applications in bioinformatics, Bayesian Model Selection for Data with High Dimension, High dimensional statistical inference: theoretical development to data analytics, Big data challenges in genomics, Analysis of microarray gene expression data using information theory and stochastic algorithm, Hybrid Models, Markov Chain Monte Carlo Methods: Theory and Practice, and more. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Statistics series - Updated release includes the latest information on Principles and Methods for Data Science

Download or read book Introduction to Statistical Machine Learning written by Masashi Sugiyama and published by Morgan Kaufmann. This book was released on 2015-10-31 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine learning allows computers to learn and discern patterns without actually being programmed. When Statistical techniques and machine learning are combined together they are a powerful tool for analysing various kinds of data in many computer science/engineering areas including, image processing, speech processing, natural language processing, robot control, as well as in fundamental sciences such as biology, medicine, astronomy, physics, and materials. Introduction to Statistical Machine Learning provides a general introduction to machine learning that covers a wide range of topics concisely and will help you bridge the gap between theory and practice. Part I discusses the fundamental concepts of statistics and probability that are used in describing machine learning algorithms. Part II and Part III explain the two major approaches of machine learning techniques; generative methods and discriminative methods. While Part III provides an in-depth look at advanced topics that play essential roles in making machine learning algorithms more useful in practice. The accompanying MATLAB/Octave programs provide you with the necessary practical skills needed to accomplish a wide range of data analysis tasks. - Provides the necessary background material to understand machine learning such as statistics, probability, linear algebra, and calculus - Complete coverage of the generative approach to statistical pattern recognition and the discriminative approach to statistical machine learning - Includes MATLAB/Octave programs so that readers can test the algorithms numerically and acquire both mathematical and practical skills in a wide range of data analysis tasks - Discusses a wide range of applications in machine learning and statistics and provides examples drawn from image processing, speech processing, natural language processing, robot control, as well as biology, medicine, astronomy, physics, and materials

Download or read book Scientific Inference Data Analysis and Robustness written by G. E. P. Box and published by Academic Press. This book was released on 2014-05-10 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Research Center Symposium: Scientific Inference, Data Analysis, and Robustness focuses on the philosophy of statistical modeling, including model robust inference and analysis of data sets. The selection first elaborates on pivotal inference and the conditional view of robustness and some philosophies of inference and modeling, including ideas on modeling, significance testing, and scientific discovery. The book then ponders on parametric empirical Bayes confidence intervals, ecumenism in statistics, and frequency properties of Bayes rules. Discussions focus on consistency of Bayes rules, scientific method and the human brain, and statistical estimation and criticism. The book takes a look at the purposes and limitations of data analysis, likelihood, shape, and adaptive inference, statistical inference and measurement of entropy, and the robustness of a hierarchical model for multinomials and contingency tables. Topics include numerical results for contingency tables and robustness, multinomials, flattening constants, and mixed Dirichlet priors, entropy and likelihood, and test as measurement of entropy. The selection is a valuable reference for researchers interested in robust inference and analysis of data sets.

Download or read book Likelihood and Bayesian Inference written by Leonhard Held and published by Springer Nature. This book was released on 2020-03-31 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.

Download or read book Applied Statistical Inference written by Leonhard Held and published by Springer Science & Business Media. This book was released on 2013-11-12 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective. A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.

Download or read book Innovations in Multivariate Statistical Modeling written by Andriëtte Bekker and published by Springer Nature. This book was released on 2022-12-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate statistical analysis has undergone a rich and varied evolution during the latter half of the 20th century. Academics and practitioners have produced much literature with diverse interests and with varying multidisciplinary knowledge on different topics within the multivariate domain. Due to multivariate algebra being of sustained interest and being a continuously developing field, its appeal breaches laterally across multiple disciplines to act as a catalyst for contemporary advances, with its core inferential genesis remaining in that of statistics. It is exactly this varied evolution caused by an influx in data production, diffusion, and understanding in scientific fields that has blurred many lines between disciplines. The cross-pollination between statistics and biology, engineering, medical science, computer science, and even art, has accelerated the vast amount of questions that statistical methodology has to answer and report on. These questions are often multivariate in nature, hoping to elucidate uncertainty on more than one aspect at the same time, and it is here where statistical thinking merges mathematical design with real life interpretation for understanding this uncertainty. Statistical advances benefit from these algebraic inventions and expansions in the multivariate paradigm. This contributed volume aims to usher novel research emanating from a multivariate statistical foundation into the spotlight, with particular significance in multidisciplinary settings. The overarching spirit of this volume is to highlight current trends, stimulate a focus on, and connect multidisciplinary dots from and within multivariate statistical analysis. Guided by these thoughts, a collection of research at the forefront of multivariate statistical thinking is presented here which has been authored by globally recognized subject matter experts.

Download or read book Modeling and Estimation of Structural Damage written by Jonathan M. Nichols and published by John Wiley & Sons. This book was released on 2016-01-08 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling and Estimation of Damage in Structures is a comprehensiveguide to solving the type of modelling and estimation problems associated with the physics of structural damage. Provides a model-based approach to damage identification Presents an in-depth treatment of probability theory and random processes Covers both theory and algorithms for implementing maximum likelihood and Bayesian estimation approaches Includes experimental examples of all detection and identification approaches Provides a clear means by which acquired data can be used to make decisions regarding maintenance and usage of a structure

Download or read book Statistical Intervals written by William Q. Meeker and published by John Wiley & Sons. This book was released on 2017-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in an easy-to-apply format Statistical intervals provide invaluable tools for quantifying sampling uncertainty. The widely hailed first edition, published in 1991, described the use and construction of the most important statistical intervals. Particular emphasis was given to intervals—such as prediction intervals, tolerance intervals and confidence intervals on distribution quantiles—frequently needed in practice, but often neglected in introductory courses. Vastly improved computer capabilities over the past 25 years have resulted in an explosion of the tools readily available to analysts. This second edition—more than double the size of the first—adds these new methods in an easy-to-apply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on: Likelihood-based statistical intervals Nonparametric bootstrap intervals Parametric bootstrap and other simulation-based intervals An introduction to Bayesian intervals Bayesian intervals for the popular binomial, Poisson and normal distributions Statistical intervals for Bayesian hierarchical models Advanced case studies, further illustrating the use of the newly described methods New technical appendices provide justification of the methods and pathways to extensions and further applications. A webpage directs readers to current readily accessible computer software and other useful information. Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition is an up-to-date working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals.

Download or read book Textual Information Access written by Eric Gaussier and published by John Wiley & Sons. This book was released on 2013-02-04 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents statistical models that have recently been developed within several research communities to access information contained in text collections. The problems considered are linked to applications aiming at facilitating information access: - information extraction and retrieval; - text classification and clustering; - opinion mining; - comprehension aids (automatic summarization, machine translation, visualization). In order to give the reader as complete a description as possible, the focus is placed on the probability models used in the applications concerned, by highlighting the relationship between models and applications and by illustrating the behavior of each model on real collections. Textual Information Access is organized around four themes: informational retrieval and ranking models, classification and clustering (regression logistics, kernel methods, Markov fields, etc.), multilingualism and machine translation, and emerging applications such as information exploration. Contents Part 1: Information Retrieval 1. Probabilistic Models for Information Retrieval, Stéphane Clinchant and Eric Gaussier. 2. Learnable Ranking Models for Automatic Text Summarization and Information Retrieval, Massih-Réza Amini, David Buffoni, Patrick Gallinari, Tuong Vinh Truong and Nicolas Usunier. Part 2: Classification and Clustering 3. Logistic Regression and Text Classification, Sujeevan Aseervatham, Eric Gaussier, Anestis Antoniadis, Michel Burlet and Yves Denneulin. 4. Kernel Methods for Textual Information Access, Jean-Michel Renders. 5. Topic-Based Generative Models for Text Information Access, Jean-Cédric Chappelier. 6. Conditional Random Fields for Information Extraction, Isabelle Tellier and Marc Tommasi. Part 3: Multilingualism 7. Statistical Methods for Machine Translation, Alexandre Allauzen and François Yvon. Part 4: Emerging Applications 8. Information Mining: Methods and Interfaces for Accessing Complex Information, Josiane Mothe, Kurt Englmeier and Fionn Murtagh. 9. Opinion Detection as a Topic Classification Problem, Juan-Manuel Torres-Moreno, Marc El-Bèze, Patrice Bellot and Fréderic Béchet.

Download or read book Naval Research Logistics written by and published by . This book was released on 1989 with total page 914 pages. Available in PDF, EPUB and Kindle. Book excerpt: The types of articles most sought after by Naval Research Logistics fall into the following classes: (i) modeling and analysis of problems motivated by current real-world applications, (ii) exploratory modeling and analysis of problems motivated by potential future real-world applications, (iii) major methodological advances, and (iv) expository pieces of exceptional clarity. Areas represented include (but are not limited to) probability, statistics, simulation, optimization, game theory,scheduling, reliability, inventory, decision analysis, and combatmodels.

Download or read book Information Retrieval Technology written by Yuexian Hou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th Information Retrieval Societies Conference, AIRS 2012, held in Tianjin, China, in December 2012. The 22 full papers and 26 poster presentations included in this volume were carefully reviewed and selected from 77 submissions. They are organized in topical sections named: IR models; evaluation and user studies; NLP for IR; machine learning and data mining; social media; IR applications; multimedia IT and indexing; collaborative and federated search; and the poster session.