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This book determines adjustable parameters in mathematical models that describe steady state or dynamic systems, presenting the most important optimization methods used for parameter estimation. It focuses on the Gauss-Newton method and its modifications for systems and processes represented by algebraic or differential equation models.
Parameter estimation. --- Gaussian processes. --- Distribution (Probability theory) --- Stochastic processes --- Estimation theory --- Stochastic systems --- Chemical engineering --- Mathematical models. --- Chemistry, Industrial --- Engineering, Chemical --- Industrial chemistry --- Engineering --- Chemistry, Technical --- Metallurgy --- Guaussian processes.
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The last book dedicated to this topic was published in 1978, and since then there have been many developments in survival analysis, Competing Risks, and in statistical methods in general. The subject is now drawing increasing interest from engineers and biologists. Written by an acknowledged expert, this book thoroughly examines the probability framework and statistical analysis of data of Competing Risks. With a dearth of modern treatments of the subject and the importance of its methods, Classical Competing Risks fills a long-standing gap in the literature with a carefully organized exposition filled with real data sets, numerous examples, and clear, readable prose.
Mathematical statistics --- Competing risks --- Failure time data analysis --- Temps entre défaillances, Analyse des --- 519.2 --- Analysis, Failure time data --- Data analysis, Failure time --- Failure analysis (Engineering) --- Survival analysis (Biometry) --- Risks, Competing --- Distribution (Probability theory) --- Estimation theory --- Random variables --- Competing risks. --- Failure time data analysis. --- Temps entre défaillances, Analyse des
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The introduction of permutation tests by R. A. Fisher relaxed the paramet ric structure requirement of a test statistic. For example, the structure of the test statistic is no longer required if the assumption of normality is removed. The between-object distance function of classical test statis tics based on the assumption of normality is squared Euclidean distance. Because squared Euclidean distance is not a metric (i. e. , the triangle in equality is not satisfied), it is not at all surprising that classical tests are severely affected by an extreme measurement of a single object. A major purpose of this book is to take advantage of the relaxation of the struc ture of a statistic allowed by permutation tests. While a variety of distance functions are valid for permutation tests, a natural choice possessing many desirable properties is ordinary (i. e. , non-squared) Euclidean distance. Sim ulation studies show that permutation tests based on ordinary Euclidean distance are exceedingly robust in detecting location shifts of heavy-tailed distributions. These tests depend on a metric distance function and are reasonably powerful for a broad spectrum of univariate and multivariate distributions. Least sum of absolute deviations (LAD) regression linked with a per mutation test based on ordinary Euclidean distance yields a linear model analysis which controls for type I error.
Mathematical statistics --- #PBIB:2003.2 --- Resampling (Statistics) --- Statistical hypothesis testing. --- Resampling (Statistics). --- Statistical hypothesis testing --- Hypothesis testing (Statistics) --- Significance testing (Statistics) --- Statistical significance testing --- Testing statistical hypotheses --- Resampling methods (Statistics) --- Distribution (Probability theory) --- Hypothesis --- Nonparametric statistics --- Statistics . --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics
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This book is a practical guide to help researchers draw valid causal inferences from small-scale clinical intervention studies. It should be of interest to teachers of, and students in, courses with an experimental clinical component, as well as clinical researchers. Inferential statistics used in the analysis of group data are frequently invalid for use with data from single-case experimental designs. Even non-parametric rank tests provide, at best, approximate solutions for only some single-case (and small-'n' ) designs. Randomization (Exact) tests, on the other hand, can provide valid statistical analyses for all designs that incorporate a random procedure for assigning treatments to subjects or observation periods, including single-case designs. These Randomization tests require large numbers of data rearrangements and have been seldom used, partly because desktop computers have only recently become powerful enough to complete the analyses in a reasonable time. Now that the necessary computational power is available, they continue to be under-used because they receive scant attention in standard statistical texts for behavioral researchers and because available programs for running the analyses are relatively inaccessible to researchers with limited statistical or computing interest. This book is first and foremost a practical guide, although it also presents the theoretical basis for Randomization tests. Its most important aim is to make these tests accessible to researchers for a wide range of designs. It does this by providing programs on CD-ROM that allow users to run analyses of their data within a standard package (Minitab, Excel, or SPSS) with which they are already familiar. No statistical or computing expertise is required to use these programs. This is the "new stats" for single-case and small-'n' intervention studies, and anyone interested in this research approach will benefit.
Experimental design. --- Statistical hypothesis testing. --- Experimental design --- Statistical hypothesis testing --- Hypothesis testing (Statistics) --- Significance testing (Statistics) --- Statistical significance testing --- Testing statistical hypotheses --- Distribution (Probability theory) --- Hypothesis --- Mathematical statistics --- Design of experiments --- Statistical design --- Mathematical optimization --- Research --- Science --- Statistical decision --- Statistics --- Analysis of means --- Analysis of variance --- Experiments --- Methodology --- Statistiek (theorie) --- Tests (geneeskunde) --- Test (geneeskunde)
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New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.
Quantum theory --- Théorie quantique --- Mathematics --- Mathématiques --- Mathematics. --- Atomic Physics --- Physics --- Physical Sciences & Mathematics --- Théorie quantique --- Mathématiques --- Quantum theory. --- Distribution (Probability theory. --- Statistical physics. --- Quantum Physics. --- Complex Systems. --- Probability Theory and Stochastic Processes. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Statistical methods --- Quantum physics. --- Dynamical systems. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics
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These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability. The basic technique employed in the derivation of many bounds is induc tive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound dis tributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexpo nential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The results obtained or the arguments employed in these situations are similar to those for the compound distributions, and thus we felt it useful to include them in the notes. In many cases we have included exact results, since these are useful in conjunction with the bounds and approximations developed.
Insurance --- Distribution (Probability theory) --- Statistical methods --- Stochastic processes --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Distribution (Théorie des probabilités) --- Statistical methods. --- Actuarial statistics --- Insurance statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematics --- Probabilities. --- Statistics . --- Economics, Mathematical . --- Probability Theory and Stochastic Processes. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Statistical analysis --- Statistical data --- Statistical science --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology --- Insurance - Statistical methods
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Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.
Stochastic processes --- Estimation theory --- Combinatorial analysis --- Distribution (Probability theory) --- 519.2 --- 519.21 --- 519.246 --- Combinatorics --- Algebra --- Mathematical analysis --- Estimating techniques --- Least squares --- Mathematical statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability. Mathematical statistics --- Probability theory. Stochastic processes --- Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- 519.246 Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- 519.21 Probability theory. Stochastic processes --- 519.2 Probability. Mathematical statistics --- Statistics . --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics
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This volume contains the papers selected for presentation at IPCO VIII, the Eighth Conference on Integer Programming and Combinatorial Optimization, Utrecht, The Netherlands, 2001. This meeting isa forum for researchers and practitioners working on various aspects of integer programming and combi- torial optimization. The aim is to present recent developments in theory, com- tation, and application of integer programming and combinatorial optimization. Topics include, but are not limited to: approximation algorithms, branch and bound algorithms, computational biology, computational complexity, compu- tional geometry, cutting plane algorithms, diophantine equations, geometry of numbers, graph and network algorithms, integer programming, matroids and submodular functions, on-line algorithms, polyhedral combinatorics, scheduling theory and algorithms, and semide nit e programs. IPCO was established in 1988 when the rs t IPCO program committee was formed. The locations and years of the seven rs t IPCO conferences were: IPCO I, Waterloo (Canada) 1990, IPCO II, Pittsburgh (USA) 1992, IPCO III, - ice (Italy) 1993, IPCO IV, Copenhagen (Denmark) 1995, IPCO V, Vancouver (Canada) 1996, IPCO VI, Houston (USA) 1998, IPCO VII, Graz (Austria) 1999. IPCO is held every year in which no MPS (Mathematical Programming Society) International Symposium takes place. Since the MPS meeting is triennial, IPCO conferences are held twice in every three-year period. Asa rule, IPCO is held somewhere in Northern America in even years, and somewhere in Europe in odd years.
Integer programming --- Combinatorial optimization --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Congresses --- Mathematics. --- Information technology. --- Business --- Algorithms. --- Computer science --- Probabilities. --- Combinatorics. --- Probability Theory and Stochastic Processes. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- IT in Business. --- Data processing. --- Programming (Mathematics) --- Distribution (Probability theory. --- Computer software. --- Computational complexity. --- Combinatorics --- Algebra --- Mathematical analysis --- IT (Information technology) --- Technology --- Telematics --- Information superhighway --- Knowledge management --- Complexity, Computational --- Electronic data processing --- Machine theory --- Software, Computer --- Computer systems --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Computer science—Mathematics. --- Business—Data processing. --- Algorism --- Arithmetic --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Foundations --- Integer programming - Congresses --- Combinatorial optimization - Congresses
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This selection of reviews and papers is intended to stimulate renewed reflection on the fundamental and practical aspects of probability in physics. While putting emphasis on conceptual aspects in the foundations of statistical and quantum mechanics, the book deals with the philosophy of probability in its interrelation with mathematics and physics in general. Addressing graduate students and researchers in physics and mathematics together with philosophers of science, the contributions avoid cumbersome technicalities in order to make the book worthwhile reading for nonspecialists and specialists alike.
Probabilities --- Quantum theory --- Statistical mechanics --- Mathematical physics --- Distribution (Probability theory. --- Quantum theory. --- Philosophy (General). --- Statistical physics. --- Complex Systems. --- Probability Theory and Stochastic Processes. --- Quantum Physics. --- Philosophy, general. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Dynamical systems. --- Probabilities. --- Quantum physics. --- Philosophy. --- Mental philosophy --- Humanities --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Risk --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics --- Probabilities - Congresses --- Quantum theory - Congresses --- Statistical mechanics - Congresses --- Mathematical physics - Congresses
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