05688nam 22007334a 450 991101935490332120200520144314.0978661034479697812803447941280344792978047030664204703066459780471475743047147574297804714757670471475769(CKB)111087027115174(EBL)468695(OCoLC)54712547(SSID)ssj0000212823(PQKBManifestationID)11234935(PQKBTitleCode)TC0000212823(PQKBWorkID)10138621(PQKB)10149308(MiAaPQ)EBC468695(Perlego)2765563(EXLCZ)9911108702711517420030513d2004 uy 0engur|n|---|||||txtccrNumerical issues in statistical computing for the social scientist /Micah Altman, Jeff Gill, Michael P. McDonaldHoboken, NJ Wileyc20041 online resource (348 p.)Wiley series in probability and statisticsDescription based upon print version of record.9780471236337 0471236330 Includes bibliographical references (p. 267-301) and indexes.Numerical Issues in Statistical Computing for the Social Scientist; Contents; Preface; 1 Introduction: Consequences of Numerical Inaccuracy; 1.1 Importance of Understanding Computational Statistics; 1.2 Brief History: Duhem to the Twenty-First Century; 1.3 Motivating Example: Rare Events Counts Models; 1.4 Preview of Findings; 2 Sources of Inaccuracy in Statistical Computation; 2.1 Introduction; 2.1.1 Revealing Example: Computing the Coefficient Standard Deviation; 2.1.2 Some Preliminary Conclusions; 2.2 Fundamental Theoretical Concepts; 2.2.1 Accuracy and Precision2.2.2 Problems, Algorithms, and Implementations2.3 Accuracy and Correct Inference; 2.3.1 Brief Digression: Why Statistical Inference Is Harder in Practice Than It Appears; 2.4 Sources of Implementation Errors; 2.4.1 Bugs, Errors, and Annoyances; 2.4.2 Computer Arithmetic; 2.5 Algorithmic Limitations; 2.5.1 Randomized Algorithms; 2.5.2 Approximation Algorithms for Statistical Functions; 2.5.3 Heuristic Algorithms for Random Number Generation; 2.5.4 Local Search Algorithms; 2.6 Summary; 3 Evaluating Statistical Software; 3.1 Introduction; 3.1.1 Strategies for Evaluating Accuracy3.1.2 Conditioning3.2 Benchmarks for Statistical Packages; 3.2.1 NIST Statistical Reference Datasets; 3.2.2 Benchmarking Nonlinear Problems with StRD; 3.2.3 Analyzing StRD Test Results; 3.2.4 Empirical Tests of Pseudo-Random Number Generation; 3.2.5 Tests of Distribution Functions; 3.2.6 Testing the Accuracy of Data Input and Output; 3.3 General Features Supporting Accurate and Reproducible Results; 3.4 Comparison of Some Popular Statistical Packages; 3.5 Reproduction of Research; 3.6 Choosing a Statistical Package; 4 Robust Inference; 4.1 Introduction; 4.2 Some Clarification of Terminology4.3 Sensitivity Tests4.3.1 Sensitivity to Alternative Implementations and Algorithms; 4.3.2 Perturbation Tests; 4.3.3 Tests of Global Optimality; 4.4 Obtaining More Accurate Results; 4.4.1 High-Precision Mathematical Libraries; 4.4.2 Increasing the Precision of Intermediate Calculations; 4.4.3 Selecting Optimization Methods; 4.5 Inference for Computationally Difficult Problems; 4.5.1 Obtaining Confidence Intervals with Ill-Behaved Functions; 4.5.2 Interpreting Results in the Presence of Multiple Modes; 4.5.3 Inference in the Presence of Instability5 Numerical Issues in Markov Chain Monte Carlo Estimation5.1 Introduction; 5.2 Background and History; 5.3 Essential Markov Chain Theory; 5.3.1 Measure and Probability Preliminaries; 5.3.2 Markov Chain Properties; 5.3.3 The Final Word (Sort of); 5.4 Mechanics of Common MCMC Algorithms; 5.4.1 Metropolis-Hastings Algorithm; 5.4.2 Hit-and-Run Algorithm; 5.4.3 Gibbs Sampler; 5.5 Role of Random Number Generation; 5.5.1 Periodicity of Generators and MCMC Effects; 5.5.2 Periodicity and Convergence; 5.5.3 Example: The Slice Sampler; 5.5.4 Evaluating WinBUGS; 5.6 Absorbing State Problem5.7 Regular Monte Carlo SimulationAt last-a social scientist's guide through the pitfalls of modern statistical computing Addressing the current deficiency in the literature on statistical methods as they apply to the social and behavioral sciences, Numerical Issues in Statistical Computing for the Social Scientist seeks to provide readers with a unique practical guidebook to the numerical methods underlying computerized statistical calculations specific to these fields. The authors demonstrate that knowledge of these numerical methods and how they are used in statistical packages is essential for making accurate inferences.Wiley series in probability and statistics.StatisticsData processingSocial sciencesStatistical methodsData processingStatisticsData processing.Social sciencesStatistical methodsData processing.519.5Altman Micah856268Gill Jeff119070McDonald Michael1967-856269MiAaPQMiAaPQMiAaPQBOOK9911019354903321Numerical issues in statistical computing for the social scientist4416406UNINA03954nam 22005655 450 991030013250332120200701114651.03-319-95363-X10.1007/978-3-319-95363-2(CKB)4100000005958479(MiAaPQ)EBC5497749(DE-He213)978-3-319-95363-2(PPN)229916627(EXLCZ)99410000000595847920180822d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierTime Optimal Control of Evolution Equations /by Gengsheng Wang, Lijuan Wang, Yashan Xu, Yubiao Zhang1st ed. 2018.Cham :Springer International Publishing :Imprint: Birkhäuser,2018.1 online resource (344 pages)PNLDE Subseries in Control ;923-319-95362-1 Preface -- Mathematical Preliminaries -- Time Optimal Control Problems -- Existence of Admissible Groups and Optimal Groups -- Maximum Principle of Optimal Groups -- Equivalence of Several Kinds of Optimal Controls -- Bang-Bang Properties of Optimal Groups -- References.This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal control problems. By discussing the best way of representing various control problems and equivalence among them, this systematic study gives readers the tools they need to solve practical problems in control. After introducing preliminaries in functional analysis, evolution equations, and controllability and observability estimates, the authors present their time-optimal control framework, which consists of four elements: a controlled system, a control constraint set, a starting set, and an ending set. From there, they use their framework to address areas of recent development in time-optimal control, including the existence of admissible controls and optimal controls, Pontryagin’s maximum principle for optimal controls, the equivalence of different optimal control problems, and bang-bang properties. This monograph will appeal to researchers and graduate students in time-optimal control theory, as well as related areas of controllability and dynamic programming. For ease of reference, the text itself is self-contained on the topic of time-optimal control. Frequent examples throughout clarify the applications of theorems and definitions, although experience with functional analysis and differential equations will be useful.PNLDE Subseries in Control ;92System theoryAutomatic controlEngineering mathematicsSystems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Control and Systems Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/T19010Engineering Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/T11030System theory.Automatic control.Engineering mathematics.Systems Theory, Control.Control and Systems Theory.Engineering Mathematics.515.353Wang Gengshengauthttp://id.loc.gov/vocabulary/relators/aut756040Wang Lijuanauthttp://id.loc.gov/vocabulary/relators/autXu Yashanauthttp://id.loc.gov/vocabulary/relators/autZhang Yubiaoauthttp://id.loc.gov/vocabulary/relators/autBOOK9910300132503321Time Optimal Control of Evolution Equations1912863UNINA