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"Today, we are facing a data rich world that is changing faster than ever before. The ubiquitous availability of data provides great opportunities for industrial enterprises to improve their process quality and productivity. Industrial data analytics is the process of collecting, exploring, and analyzing data generated from industrial operations and throughout the product life cycle in order to gain insights and improve decision-making. This book describes industrial data analytics approaches with an emphasis on diagnosis and prognosis of industrial processes and systems. A large number of textbooks/research monographs exist on diagnosis and prognosis in the engineering eld. Most of these engineering books focus on model-based diagnosis and prognosis problems in dynamic systems. The modelbased approaches adopt a dynamic model for the system, often in the form of a state space model, as the basis for diagnosis and prognosis. Dierent from these existing books, this book focuses on the concept of random effects and its applications in system diagnosis and prognosis. The impetus for this book arose from the current digital revolution. In this digital age, the essential feature of a modern engineering system is that a large amount of data from multiple similar units/machines during their operations are collected in real time. This feature poses signicant intellectual opportunities and challenges. As for opportunities, since we have observations from potentially a very large number of similar units, we can compare their operations, share the information, and extract common knowledge to enable accurate and tailored prediction and control at the individual level. As for challenges, because the data are collected in the field and not in a controlled environment, the data contain signicant variation and heterogeneity due to the large variations in working/usage conditions for dierent units. This requires that the analytics approaches should be not only general (so that the common information can be learned and shared), but also flexible (so that the behaviour of an individual unit can be captured and controlled). The random effects modeling approaches can exactly address these opportunities and challenges"--
Random data (Statistics) --- Industrial management --- Industrial engineering --- Mathematics. --- Statistical methods.
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"This book, written by three behavioral scientists for other behavioral scientists, addresses common issues in statistical analysis for the behavioral and educational sciences. Modern Statistical & Computing Methods for the Behavioral and Educational Sciences using R emphasizes the direct link between scientific research questions and data analysis. Purposeful attention is paid to the integration of design, statistical methodology, and computation to propose answers to specific research questions. Furthermore, practical suggestions for the analysis and presentation of results, in prose, tables and/or figures, are included. Optional sections for each chapter include methodological extensions for readers desiring additional technical details. Rather than focus on mathematical calculations like so many other introductory texts in the behavioral sciences, the authors focus on conceptual explanations and the use of statistical computing. Statistical computing is an integral part of statistical work, and to support student learning in this area, examples using the R computer program are provided throughout the book. Rather than relegate examples to the end of chapters, the authors interweave computer examples with the narrative of the book. Topical coverage includes an introduction to R, data exploration of one variable, data exploration of multivariate data - comparing two groups and many groups, permutation and randomization tests, the independent samples t-Test, the Bootstrap test, interval estimates and effect sizes, power, and dependent samples"--
Bootstrap (Statistics) --- Distribution (Probability theory) --- Psychology --- Random data (Statistics) --- R (Computer program language) --- Data processing
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Stochastic programming. --- Mathematical optimization. --- Numbers, Random. --- Random numbers --- Random sampling numbers --- Random data (Statistics) --- Sampling (Statistics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Linear programming
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Random effects and latent variable models are broadly used in analyses of multivariate data. These models can accommodate high dimensional data having a variety of measurement scales. Methods for model selection and comparison are needed in conducting hypothesis tests and in building sparse predictive models. However, classical methods for model comparison are not well justified in such settings. This book presents state of the art methods for accommodating model uncertainty in random effects and latent variable models. It will appeal to students, applied data analysts, and experienced researchers. The chapters are based on the contributors’ research, with mathematical details minimized using applications-motivated descriptions. The first part of the book focuses on frequentist likelihood ratio and score tests for zero variance components. Contributors include Xihong Lin, Daowen Zhang and Ciprian Crainiceanu. The second part focuses on Bayesian methods for random effects selection in linear mixed effects and generalized linear mixed models. Contributors include David Dunson and collaborators Bo Cai and Saki Kinney. The final part focuses on structural equation models, with Peter Bentler and Jiajuan Liang presenting a frequentist approach, Sik-Yum Lee and Xin-Yuan Song presenting a Bayesian approach based on path sampling, and Joyee Ghosh and David Dunson proposing a method for default prior specification and efficient posterior computation. David Dunson is Professor in the Department of Statistical Science at Duke University. He is an international authority on Bayesian methods for correlated data, a fellow of the American Statistical Association, and winner of the David Byar and Mortimer Spiegelman Awards.
Statistics. --- Statistical Theory and Methods. --- Mathematical statistics. --- Statistique --- Statistique mathématique --- Electronic books. -- local. --- Latent variables. --- Random data (Statistics). --- Latent variables --- Random data (Statistics) --- Mathematics --- Mathematical Statistics --- Physical Sciences & Mathematics --- Data, Random (Statistics) --- Constructs, Hypothetical --- Hypothetical constructs --- Variables, Latent --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Statistics --- Stochastic processes --- Latent structure analysis --- Multivariate analysis --- Variables (Mathematics) --- Distribution (Probability theory. --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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Decision Systems and Nonstochastic Randomness presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models. Each self-contained chapter of this neatly-structured monograph includes a detailed introduction and summary of its contents. The included results are presented not only with rigorous proofs but also through numerous intuitive examples. An appendix is provided which includes classic results from the theory of functions and measured sets as well as decision theory, offering an overview of the necessary prerequisites. The formalism of statistical regularities developed in this book will have a significant influence on decision theory and information theory as well as numerous other disciplines. Because of these far-reaching implications, this book may be a useful resource for statisticians, mathematicians, engineers, economists and other utilizing nonstochastic modeling and decision theory.
Mathematics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Game Theory, Economics, Social and Behav. Sciences. --- Operations Research/Decision Theory. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Distribution (Probability theory). --- Mathematical statistics. --- Economics --- Mathématiques --- Distribution (Théorie des probabilités) --- Statistique mathématique --- Statistics. --- Statistical decision --- Random data (Statistics) --- Random dynamical systems
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Mathematical statistics --- Computer simulation --- Simulation par ordinateur --- 519.876 --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Theory of large systems --- Computer simulation. --- 519.876 Theory of large systems --- COMPUTER SIMULATION --- Simulation software --- STATISTICS --- Non - uniform distributions --- Random numbers --- Monograph --- Statistics. --- Numbers, Random. --- Random sampling numbers --- Random data (Statistics) --- Sampling (Statistics) --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics
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519.2 --- Computational complexity --- Data encryption (Computer science) --- Numbers, Random --- Random number generators --- #TELE:COSIC --- 681.3*E3 --- Generators, Random number --- Electronic digital computers --- Random numbers --- Random sampling numbers --- Random data (Statistics) --- Sampling (Statistics) --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Complexity, Computational --- Electronic data processing --- Machine theory --- Probability. Mathematical statistics --- Data encryption: data encryption standard; DES; public key cryptosystems --- 681.3*E3 Data encryption: data encryption standard; DES; public key cryptosystems --- 519.2 Probability. Mathematical statistics --- Coding theory. --- Codage. --- Générateurs de nombres aléatoires --- Random number generators. --- Codage --- Générateurs de nombres aléatoires. --- Cryptographie
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Monte Carlo method --- Numbers, Random --- Random number generators --- 519.245 --- 681.3*G3 --- Generators, Random number --- Electronic digital computers --- Random numbers --- Random sampling numbers --- Random data (Statistics) --- Sampling (Statistics) --- Artificial sampling --- Model sampling --- Monte Carlo simulation --- Monte Carlo simulation method --- Stochastic sampling --- Games of chance (Mathematics) --- Mathematical models --- Numerical analysis --- Numerical calculations --- Stochastic processes --- 519.245 Stochastic approximation. Monte Carlo methods --- Stochastic approximation. Monte Carlo methods --- 681.3*G3 Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing) --- Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing) --- Probability theory
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“Decision Systems and Nonstochastic Randomness” presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models. Each self-contained chapter of this neatly-structured monograph includes a detailed introduction and summary of its contents. The included results are presented not only with rigorous proofs but also through numerous intuitive examples. An appendix is provided which includes classic results from the theory of functions and measured sets as well as decision theory, offering an overview of the necessary prerequisites. The formalism of statistical regularities developed in this book will have a significant influence on decision theory and information theory as well as numerous other disciplines. Because of these far-reaching implications, this book may be a useful resource for statisticians, mathematicians, engineers, economists and other utilizing nonstochastic modeling and decision theory.
Random data (Statistics). --- Random dynamical systems. --- Statistical decision. --- Statistical decision --- Random data (Statistics) --- Random dynamical systems --- Mathematics --- Mathematical Statistics --- Physical Sciences & Mathematics --- Dynamical systems, Random --- Data, Random (Statistics) --- Decision problems --- Mathematics. --- Operations research. --- Decision making. --- Business mathematics. --- Applied mathematics. --- Engineering mathematics. --- Game theory. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Business Mathematics. --- Statistical Theory and Methods. --- Game Theory, Economics, Social and Behav. Sciences. --- Operation Research/Decision Theory. --- Differentiable dynamical systems --- Statistics --- Stochastic processes --- Game theory --- Operations research --- Management science --- Distribution (Probability theory. --- Mathematical statistics. --- Operations Research/Decision Theory. --- Operational analysis --- Operational research --- Industrial engineering --- Research --- System theory --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Statistics . --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Games, Theory of --- Theory of games --- Mathematical models --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Decision making
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Formal languages --- Langages formels --- Congresses. --- Congrès --- Mathematical Theory --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Numbers, Random --- Random numbers --- Random sampling numbers --- Computer science. --- Computers. --- Computer logic. --- Mathematical logic. --- Computer science --- Computer Science. --- Mathematical Logic and Formal Languages. --- Computation by Abstract Devices. --- Logics and Meanings of Programs. --- Discrete Mathematics in Computer Science. --- Symbolic and Algebraic Manipulation. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer science logic --- Logic, Symbolic and mathematical --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Informatics --- Science --- Random data (Statistics) --- Sampling (Statistics) --- Logic design. --- Computational complexity. --- Data processing. --- Complexity, Computational --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Computer science—Mathematics. --- Machine theory. --- Discrete mathematics. --- Formal Languages and Automata Theory. --- Theory of Computation. --- Computer Science Logic and Foundations of Programming. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Recursive functions --- Robotics
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