نام کتاب | Evolutionary Statistical Procedures: An Evolutionary Computation Approach to Statistical Procedures Designs and Applications |

ISBN | 9783642162183 |

نويسنده | Roberto Baragona:Francesco Battaglia:Irene Poli |

ناشر | Springer |

سال انتشار | 2011 |

تعداد صفحات | 289 |

اندازه فايل | 3.4 |

فرمت کتاب | |

لينک دانلود | Evolutionary Statistical Procedures: An Evolutionary Computation Approach to Statistical Procedures Designs and Applications |

This proposed text appears to be a good introduction to evolutionary computation for use in applied statistics research. The authors draw from a vast base of knowledge about the current literature in both the design of evolutionary algorithms and statistical techniques. Modern statistical research is on the threshold of solving increasingly complex problems in high dimensions, and the generalization of its methodology to parameters whose estimators do not follow mathematically simple distributions is underway. Many of these challenges involve optimizing functions for which analytic solutions are infeasible. Evolutionary algorithms represent a powerful and easily understood means of approximating the optimum value in a variety of settings. The proposed text seeks to guide readers through the crucial issues of optimization problems in statistical settings and the implementation of tailored methods (including both stand-alone evolutionary algorithms and hybrid crosses of these procedures with standard statistical algorithms like Metropolis-Hastings) in a variety of applications. This book would serve as an excellent reference work for statistical researchers at an advanced graduate level or beyond, particularly those with a strong background in computer science.

نام کتاب | Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions |

ISBN | 9780387946887 |

نويسنده | Martin A. Tanner |

ناشر | Springer |

سال انتشار | 1996 |

تعداد صفحات | 213 |

اندازه فايل | 19.1 |

فرمت کتاب | |

لينک دانلود | Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions |

A unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. This third edition expands the discussion of many of the techniques presented, and includes additional examples as well as exercise sets at the end of each chapter.

نام کتاب | Hybrid Random Fields: A Scalable Approach to Structure and Parameter Learning in Probabilistic Graphical Models |

ISBN | 3642203078 |

نويسنده | Antonino Freno:Edmondo Trentin |

ناشر | Springer |

سال انتشار | 2011 |

تعداد صفحات | 217 |

اندازه فايل | 2.2 |

فرمت کتاب | |

لينک دانلود | Hybrid Random Fields: A Scalable Approach to Structure and Parameter Learning in Probabilistic Graphical Models |

This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives.

-- Manfred Jaeger, Aalborg Universitet

The book not only marks an effective direction of investigation with significant experimental advances, but it is also---and perhaps primarily---a guide for the reader through an original trip in the space of probabilistic modeling. While digesting the book, one is enriched with a very open view of the field, with full of stimulating connections. [...] Everyone specifically interested in Bayesian networks and Markov random fields should not miss it.

-- Marco Gori, Università degli Studi di Siena

Graphical models are sometimes regarded---incorrectly---as an impractical approach to machine learning, assuming that they only work well for low-dimensional applications and discrete-valued domains. While guiding the reader through the major achievements of this research area in a technically detailed yet accessible way, the book is concerned with the presentation and thorough (mathematical and experimental) investigation of a novel paradigm for probabilistic graphical modeling, the hybrid random field. This model subsumes and extends both Bayesian networks and Markov random fields. Moreover, it comes with well-defined learning algorithms, both for discrete and continuous-valued domains, which fit the needs of real-world applications involving large-scale, high-dimensional data.

This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives.

-- Manfred Jaeger, Aalborg Universitet

The book not only marks an effective direction of investigation with significant experimental advances, but it is also---and perhaps primarily---a guide for the reader through an original trip in the space of probabilistic modeling. While digesting the book, one is enriched with a very open view of the field, with full of stimulating connections. [...] Everyone specifically interested in Bayesian networks and Markov random fields should not miss it.

-- Marco Gori, Università degli Studi di Siena

Graphical models are sometimes regarded---incorrectly---as an impractical approach to machine learning, assuming that they only work well for low-dimensional applications and discrete-valued domains. While guiding the reader through the major achievements of this research area in a technically detailed yet accessible way, the book is concerned with the presentation and thorough (mathematical and experimental) investigation of a novel paradigm for probabilistic graphical modeling, the hybrid random field. This model subsumes and extends both Bayesian networks and Markov random fields. Moreover, it comes with well-defined learning algorithms, both for discrete and continuous-valued domains, which fit the needs of real-world applications involving large-scale, high-dimensional data.

نام کتاب | Dynamical Inverse Problems: Theory and Application |

ISBN | 3709106958 |

نويسنده | Graham M. L. Gladwell:Antonino Morassi |

ناشر | Springer |

سال انتشار | 2011 |

تعداد صفحات | 229 |

اندازه فايل | 3.2 |

فرمت کتاب | |

لينک دانلود | Dynamical Inverse Problems: Theory and Application |

The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.

نام کتاب | Applied Probability |

ISBN | 0387004254 |

نويسنده | Kenneth Lange |

ناشر | Springer |

سال انتشار | 2003 |

تعداد صفحات | 390 |

اندازه فايل | 2.1 |

فرمت کتاب | |

لينک دانلود | {accesstext mode="level" level="registered"} برای مشاهده لینک دانلود لطفاً وارد سایت شوید||Applied Probability {/accesstext} |

This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material here for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. Finally, Chapters 12 and 13 develop the Chen-Stein method of Poisson approximation and connections between probability and number theory. Kenneth Lange is Professor of Biomathematics and Human Genetics and Chair of the Department of Human Genetics at the UCLA School of Medicine. He has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Springer-Verlag published his books Numerical Analysis for Statisticians and Mathematical and Statistical Methods for Genetic Analysis Second Edition, in 1999 and 2002, respectively.

From the reviews:

"This book was written to convey both the 'beauty and utility of probability.' The author achieves this by providing a mixture of theory and application. To include so many different and interesting applications of probability, the author chose to minimize the number of proofs. Instead, he provides examples and written explanations…The unique aspect of this text is that the author presents applications not normally included in probability texts. There are new and very useful applications of probability that would usually be found in journal articles or in a number of different textbooks." Technometrics, May 2004

"…Pretty applications in computer science and genetics strengthen the overall message of this book, namely to give applied probability the attention it deserves." Short Book Reviews of the International Statistical Institute, April 2004

"In his Preface, he worries that the pursuit of mathematical rigor discourages students of science, particularly of biology, from learning the powerful tools that modern probability theory puts at their disposal. This book is an attempt to remedy that…Professor Lange’s book is certainly a pleasure to read, and it is written in a clear style using standard probabilistic notation." Journal of the American Statistical Association, June 2004

"This book is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics and statistics. … The book presents a mixture of theory and applications, with emphasis on mathematical modeling and computational techniques. It contains a number of examples from the biological sciences. … All chapters have exercises and hints are provided for some of the difficult problems. … Students should find this book stimulating, refreshing and highly useful." (R. Subramanian, Mathematical Reviews, 2004a)

"The book would be a delight to use. … Lange has produced an enjoyable, highly readable book … . I found much of the material of interest … . All of the chapters come with exercises some of them challenging. … a course based on this material would be a joy." (Jeffrey J. Hunter, New Zealand Mathematical Society Newsletter, Issue 89, December, 2003)

"Lange makes every possible effort to keep a delicate balance between theory and applications. He presents the material in a clear and informative manner that will appeal to all interested readers … . Lange offers numerous illustrative examples from biological sciences and challenging chapter end problems. This interesting and useful book presents clearly the applicability of probabilistic tools to solve problems in different disciplines. Summing Up: Recommended. Researchers and graduate students in genetics, mathematics, physics, biostatistics, computer science, and statistics." (D.V. Chopra, CHOICE, September, 2003)

"The author tries to offer to the scientific community at large an introduction to some of the most important aspects of applied probability. From the table of contents, it is clear that the author has chosen a very personal approach … . this choice illustrates the beauty, utility and relevance of probabilistic thinking in a variety of scientific areas. In particular, pretty applications in computer science and genetics strengthen the overall message of this book, namely to give applied probability the attention it deserves." (J.L. Teugels, Short Book Reviews, Vol. 24 (1), 2004)

Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. It can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. The second edition adds two new chapters on asymptotic and numerical methods and an appendix that separates some of the more delicate mathematical theory from the steady flow of examples in the main text. Besides the two new chapters, the second edition includes a more extensive list of exercises, many additions to the exposition of combinatorics, new material on rates of convergence to equilibrium in reversible Markov chains, a discussion of basic reproduction numbers in population modeling, and better coverage of Brownian motion. Because many chapters are nearly self-contained, mathematical scientists from a variety of backgrounds will find Applied Probability useful as a reference. Kenneth Lange is the Rosenfeld Professor of Computational Genetics in the Departments of Biomathematics and Human Genetics at the UCLA School of Medicine and the Chair of the Department of Human Genetics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, high-dimensional optimization, and applied stochastic processes. Springer previously published his books Mathematical and Statistical Methods for Genetic Analysis, 2nd ed., Numerical Analysis for Statisticians, 2nd ed., and Optimization. He has written over 200 research papers and produced with his UCLA colleague Eric Sobel the computer program Mendel, widely used in statistical genetics.

نام کتاب | Intelligent Mathematics: Computational Analysis |

ISBN | 3642170978 |

نويسنده | George A. Anastassiou |

ناشر | Springer |

سال انتشار | 2010 |

تعداد صفحات | 793 |

اندازه فايل | 5.7 |

فرمت کتاب | |

لينک دانلود | {accesstext mode="level" level="registered"} برای مشاهده لینک دانلود لطفاً وارد سایت شوید||Intelligent Mathematics: Computational Analysis {/accesstext} |

Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.

From the reviews:

“G. A. Anastassiou is a very prolific author. His work, which has appeared in 83 papers and books during the period 1990-2010, is restructured and completed to form the 45 chapters (plus an introductory survey) of this monograph. Each chapter is self-contained and can be read independently. … The book has the advantage of bringing together the work of the author in a systematic way, and hence it is quite useful for researchers working in this direction.” (A. Bultheel, Mathematical Reviews, January, 2013)

PLEASE USE THE FILE BACK COVER!

Knowledge can be modelled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators.We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals.We further deal with semigroup operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations.We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities.We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities.We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.

نام کتاب | Statistics and Data Analysis for Financial Engineering |

ISBN | 1441977864 |

نويسنده | David Ruppert |

ناشر | Springer |

سال انتشار | 2010 |

تعداد صفحات | 662 |

اندازه فايل | 11.9 |

فرمت کتاب | |

لينک دانلود | {accesstext mode="level" level="registered"} برای مشاهده لینک دانلود لطفاً وارد سایت شوید||Statistics and Data Analysis for Financial Engineering {/accesstext} |

Financial engineers have access to enormous quantities of data but need powerful methods for extracting quantitative information, particularly about volatility and risks. Key features of this textbook are: illustration of concepts with financial markets and economic data, R Labs with real-data exercises, and integration of graphical and analytic methods for modeling and diagnosing modeling errors. Despite some overlap with the author's undergraduate textbook Statistics and Finance: An Introduction, this book differs from that earlier volume in several important aspects: it is graduate-level; computations and graphics are done in R; and many advanced topics are covered, for example, multivariate distributions, copulas, Bayesian computations, VaR and expected shortfall, and cointegration.

The prerequisites are basic statistics and probability, matrices and linear algebra, and calculus.

Some exposure to finance is helpful.

From the reviews:

“Book under review is aimed at Master’s students in a financial engineering program and spans the gap between some very basic finance concepts and some very advanced statistical concepts … . The book is evidently intended as, and is best approached as, a kind of working text, giving students the opportunity to work in detail through a variety of examples. The substantial chapters on regression and time series are particularly helpful in this regard. There is lots of useful R code and many example analyses.” (R. A. Maller, Mathematical Reviews, Issue 2012 d)

Financial engineers have access to enormous quantities of data but need powerful methods for extracting quantitative information, particularly about volatility and risks. Key features of this textbook are: illustration of concepts with financial markets and economic data, R Labs with real-data exercises, and integration of graphical and analytic methods for modeling and diagnosing modeling errors. Despite some overlap with the author's undergraduate textbook Statistics and Finance: An Introduction, this book differs from that earlier volume in several important aspects: it is graduate-level; computations and graphics are done in R; and many advanced topics are covered, for example, multivariate distributions, copulas, Bayesian computations, VaR and expected shortfall, and cointegration. The prerequisites are basic statistics and probability, matrices and linear algebra, and calculus. Some exposure to finance is helpful.

David Ruppert is Andrew Schultz, Jr., Professor of Engineering and Professor of Statistical Science, School of Operations Research and Information Engineering, Cornell University, where he teaches statistics and financial engineering and is a member of the Program in Financial Engineering. His research areas include asymptotic theory, semiparametric regression, functional data analysis, biostatistics, model calibration, measurement error, and astrostatistics. Professor Ruppert received his PhD in Statistics at Michigan State University. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and won the Wilcoxon prize. He is Editor of the Electronic Journal of Statistics, former Editor of the Institute of Mathematical Statistics's Lecture Notes--Monographs Series, and former Associate Editor of several major statistics journals. Professor Ruppert has published over 100 scientific papers and four books: Transformation and Weighting in Regression, Measurement Error in Nonlinear Models, Semiparametric Regression, and Statistics and Finance: An Introduction.

نام کتاب | Ubiquitous Computing Fundamentals |

ISBN | 1420093606 |

نويسنده | John Krumm |

ناشر | Chapman & Hall/CRC |

سال انتشار | 2010 |

تعداد صفحات | 410 |

اندازه فايل | 7.9 |

فرمت کتاب | |

لينک دانلود | {accesstext mode="level" level="registered"} برای مشاهده لینک دانلود لطفاً وارد سایت شوید||Ubiquitous Computing Fundamentals {/accesstext} |

"…a must-read text that provides a historical lens to see how ubicomp has matured into a multidisciplinary endeavor. It will be an essential reference to researchers and those who want to learn more about this evolving field."-From the Foreword, Professor Gregory D. Abowd, Georgia Institute of TechnologyFirst introduced two decades ago, the term ubiquitous computing is now part of the common vernacular. Ubicomp, as it is commonly called, has grown not just quickly but broadly so as to encompass a wealth of concepts and technology that serves any number of purposes across all of human endeavor. While such growth is positive, the newest generation of ubicomp practitioners and researchers, isolated to specific tasks, are in danger of losing their sense of history and the broader perspective that has been so essential to the field’s creativity and brilliance.Under the guidance of John Krumm, an original ubicomp pioneer, Ubiquitous Computing Fundamentals brings together eleven ubiquitous computing trailblazers who each report on his or her area of expertise. Starting with a historical introduction, the book moves on to summarize a number of self-contained topics. Taking a decidedly human perspective, the book includes discussion on how to observe people in their natural environments and evaluate the critical points where ubiquitous computing technologies can improve their lives. Among a range of topics this book examines:How to build an infrastructure that supports ubiquitous computing applications Privacy protection in systems that connect personal devices and personal informationMoving from the graphical to the ubiquitous computing user interfaceTechniques that are revolutionizing the way we determine a person’s location and understand other sensor measurementsWhile we needn’t become expert in every sub-discipline of ubicomp, it is necessary that we appreciate all the perspectives that make up the field and understand how our work can influence and be influenced by those perspectives. This is important, if we are to encourage future generations to be as successfully innovative as the field’s originators.

نام کتاب | A Primer on Scientific Programming With Python |

ISBN | 3642024742 |

نويسنده | Hans Petter Langtangen |

ناشر | Springer |

سال انتشار | 2009 |

تعداد صفحات | 726 |

اندازه فايل | 6.8 |

فرمت کتاب | |

لينک دانلود | {accesstext mode="level" level="registered"} برای مشاهده لینک دانلود لطفاً وارد سایت شوید||A Primer on Scientific Programming With Python {/accesstext} |

The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example- and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology, and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background, and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science.

نام کتاب | Towards Intelligent Modeling: Statistical Approximation Theory |

ISBN | 3642198252 |

نويسنده | George A. Anastassiou:Oktay Duman |

ناشر | Springer |

سال انتشار | 2011 |

تعداد صفحات | 239 |

اندازه فايل | 2.0 |

فرمت کتاب | |

لينک دانلود | {accesstext mode="level" level="registered"} برای مشاهده لینک دانلود لطفاً وارد سایت شوید||Towards Intelligent Modeling: Statistical Approximation Theory {/accesstext} |

The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught.

The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.

From the reviews:

“This is the first monograph in statistical approximation theory and fuzziness, which contains mostly the recent joint works of the authors … . The book consists of eighteen chapters which are self-contained and include many significant applications. … A complete list of references and a useful index are presented at the end of the book. This monograph is recommended to graduate students and researchers, in both pure and applied mathematics, specializing in summability and approximation theories.” (Cihan Orhan, Mathematical Reviews, Issue 2012 k)

The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught.

The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.