Handbook of Probabilistic Models carefully examines the application of advanced probabilistic models in conventional engineering fields. In this comprehensive handbook, practitioners, researchers and scientists will find detailed explanations of technical concepts, applications of the proposed methods, and the respective scientific approaches needed to solve the problem. This book provides an interdisciplinary approach that creates advanced probabilistic models for engineering fields, ranging from conventional fields of mechanical engineering and civil engineering, to electronics, electrical, earth sciences, climate, agriculture, water resource, mathematical sciences and computer sciences. Specific topics covered include minimax probability machine regression, stochastic finite element method, relevance vector machine, logistic regression, Monte Carlo simulations, random matrix, Gaussian process regression, Kalman filter, stochastic optimization, maximum likelihood, Bayesian inference, Bayesian update, kriging, copula-statistical models, and more. Explains the application of advanced probabilistic models encompassing multidisciplinary research Applies probabilistic modeling to emerging areas in engineering Provides an interdisciplinary approach to probabilistic models and their applications, thus solving a wide range of practical problems

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.

"This is a valuable reference guide for readers interested in gaining a basic understanding of probability theory or its applications in problem solving in the other disciplines." —CHOICE Providing cutting-edge perspectives and real-world insights into the greater utility of probability and its applications, the Handbook of Probability offers an equal balance of theory and direct applications in a non-technical, yet comprehensive, format. Editor Tamás Rudas and the internationally-known contributors present the material in a manner so that researchers of various backgrounds can use the reference either as a primer for understanding basic probability theory or as a more advanced research tool for specific projects requiring a deeper understanding. The wide-ranging applications of probability presented make it useful for scholars who need to make interdisciplinary connections in their work. Key Features Contains contributions from the international who′s-who of probability across several disciplines Offers an equal balance of theory and applications Explains the most important concepts of probability theory in a non-technical yet comprehensive way Provides in-depth examples of recent applications in the social and behavioral sciences as well as education, business, and law Intended Audience This Handbook makes an ideal library purchase. In addition, this volume should also be of interest to individual scholars in the social and behavioral sciences.

In this text, experts provide a complete sourcebook on methods for addressing variability and uncertainty in exposure analysis.

THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability. The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introduction, historical background, theory and applications, algorithms, and exercises. The Handbook of Probability offers coverage of: Probability Space Probability Measure Random Variables Random Vectors in Rn Characteristic Function Moment Generating Function Gaussian Random Vectors Convergence Types Limit Theorems The Handbook of Probability is an ideal resource for researchers and practitioners in numerous fields, such as mathematics, statistics, operations research, engineering, medicine, and finance, as well as a useful text for graduate students.

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.

Model checking is a computer-assisted method for the analysis of dynamical systems that can be modeled by state-transition systems. Drawing from research traditions in mathematical logic, programming languages, hardware design, and theoretical computer science, model checking is now widely used for the verification of hardware and software in industry. The editors and authors of this handbook are among the world's leading researchers in this domain, and the 32 contributed chapters present a thorough view of the origin, theory, and application of model checking. In particular, the editors classify the advances in this domain and the chapters of the handbook in terms of two recurrent themes that have driven much of the research agenda: the algorithmic challenge, that is, designing model-checking algorithms that scale to real-life problems; and the modeling challenge, that is, extending the formalism beyond Kripke structures and temporal logic. The book will be valuable for researchers and graduate students engaged with the development of formal methods and verification tools.