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Author: Jorma Rissanen
Publisher: Springer Science & Business Media
ISBN: 0387688129
Category : Mathematics
Languages : en
Pages : 145
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Book Description
No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
Author: Jorma Rissanen
Publisher: Springer Science & Business Media
ISBN: 0387688129
Category : Mathematics
Languages : en
Pages : 145
Get Book
Book Description
No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
Author: Jorma Rissanen
Publisher: World Scientific
ISBN: 9814507407
Category : Technology & Engineering
Languages : en
Pages : 191
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Book Description
This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of 'true' data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression.
Author: Pierre Duchesne
Publisher: Springer Science & Business Media
ISBN: 9780387245546
Category : Business & Economics
Languages : en
Pages : 354
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Book Description
STATISTICAL MODELING AND ANALYSIS FOR COMPLEX DATA PROBLEMS treats some of today’s more complex problems and it reflects some of the important research directions in the field. Twenty-nine authors—largely from Montreal’s GERAD Multi-University Research Center and who work in areas of theoretical statistics, applied statistics, probability theory, and stochastic processes—present survey chapters on various theoretical and applied problems of importance and interest to researchers and students across a number of academic domains. Some of the areas and topics examined in the volume are: an analysis of complex survey data, the 2000 American presidential election in Florida, data mining, estimation of uncertainty for machine learning algorithms, interacting stochastic processes, dependent data & copulas, Bayesian analysis of hazard rates, re-sampling methods in a periodic replacement problem, statistical testing in genetics and for dependent data, statistical analysis of time series analysis, theoretical and applied stochastic processes, and an efficient non linear filtering algorithm for the position detection of multiple targets. The book examines the methods and problems from a modeling perspective and surveys the state of current research on each topic and provides direction for further research exploration of the area.
Author: Pietro Mantovan
Publisher: Springer Science & Business Media
ISBN: 8847013860
Category : Computers
Languages : en
Pages : 164
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Book Description
Selected from the conference "S.Co.2009: Complex Data Modeling and Computationally Intensive Methods for Estimation and Prediction," these 20 papers cover the latest in statistical methods and computational techniques for complex and high dimensional datasets.
Author: Jianqing Fan
Publisher: CRC Press
ISBN: 1466510854
Category : Mathematics
Languages : en
Pages : 752
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Book Description
Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
Author: Sadanori Konishi
Publisher: Springer Science & Business Media
ISBN: 9780387718873
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Statistical modeling is a critical tool in scientific research. This book provides comprehensive explanations of the concepts and philosophy of statistical modeling, together with a wide range of practical and numerical examples. The authors expect this work to be of great value not just to statisticians but also to researchers and practitioners in various fields of research such as information science, computer science, engineering, bioinformatics, economics, marketing and environmental science. It’s a crucial area of study, as statistical models are used to understand phenomena with uncertainty and to determine the structure of complex systems. They’re also used to control such systems, as well as to make reliable predictions in various natural and social science fields.
Author: Anna Maria Paganoni
Publisher: Springer
ISBN: 3319111493
Category : Mathematics
Languages : en
Pages : 209
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Book Description
The book is addressed to statisticians working at the forefront of the statistical analysis of complex and high dimensional data and offers a wide variety of statistical models, computer intensive methods and applications: network inference from the analysis of high dimensional data; new developments for bootstrapping complex data; regression analysis for measuring the downsize reputational risk; statistical methods for research on the human genome dynamics; inference in non-euclidean settings and for shape data; Bayesian methods for reliability and the analysis of complex data; methodological issues in using administrative data for clinical and epidemiological research; regression models with differential regularization; geostatistical methods for mobility analysis through mobile phone data exploration. This volume is the result of a careful selection among the contributions presented at the conference "S.Co.2013: Complex data modeling and computationally intensive methods for estimation and prediction" held at the Politecnico di Milano, 2013. All the papers published here have been rigorously peer-reviewed.
Author: Andrea Scharnhorst
Publisher: Springer Science & Business Media
ISBN: 3642230687
Category : Social Science
Languages : en
Pages : 270
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Book Description
Models of Science Dynamics aims to capture the structure and evolution of science, the emerging arena in which scholars, science and the communication of science become themselves the basic objects of research. In order to capture the essence of phenomena as diverse as the structure of co-authorship networks or the evolution of citation diffusion patterns, such models can be represented by conceptual models based on historical and ethnographic observations, mathematical descriptions of measurable phenomena, or computational algorithms. Despite its evident importance, the mathematical modeling of science still lacks a unifying framework and a comprehensive study of the topic. This volume fills this gap, reviewing and describing major threads in the mathematical modeling of science dynamics for a wider academic and professional audience. The model classes presented cover stochastic and statistical models, system-dynamics approaches, agent-based simulations, population-dynamics models, and complex-network models. The book comprises an introduction and a foundational chapter that defines and operationalizes terminology used in the study of science, as well as a review chapter that discusses the history of mathematical approaches to modeling science from an algorithmic-historiography perspective. It concludes with a survey of remaining challenges for future science models and their relevance for science and science policy.
Author: K.D. Sen
Publisher: Springer Science & Business Media
ISBN: 9048138906
Category : Science
Languages : en
Pages : 304
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Book Description
The understanding of electron density as the carrier of all the information of a multielectronic system is implicit in the theorems of density functional theory. Information theoretical based measures giving a quantitative understanding of statistical complexity of such systems is shaping up as a new area of research in chemical physics. This book is the first monograph of its kind covering the aspects of complexity measure in atoms and molecules.
Author:
Publisher:
ISBN: 9788847013926
Category :
Languages : en
Pages : 176
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Book Description
