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Books > Science & Mathematics > Mathematics > Probability & statistics

Computational Genome Analysis - An Introduction (Hardcover, 1st ed. 2005. Corr. 3rd printing 2007): Richard C. Deonier, Simon... Computational Genome Analysis - An Introduction (Hardcover, 1st ed. 2005. Corr. 3rd printing 2007)
Richard C. Deonier, Simon Tavare, Michael S Waterman
R2,625 Discovery Miles 26 250 Ships in 12 - 17 working days

This book presents the foundations of key problems in computational molecular biology and bioinformatics. It focuses on computational and statistical principles applied to genomes, and introduces the mathematics and statistics that are crucial for understanding these applications. The book features a free download of the R software statistics package and the text provides great crossover material that is interesting and accessible to students in biology, mathematics, statistics and computer science. More than 100 illustrations and diagrams reinforce concepts and present key results from the primary literature. Exercises are given at the end of chapters.

Markov Random Field Modeling in Image Analysis (Hardcover, 3rd ed. 2009): Stan Z. Li Markov Random Field Modeling in Image Analysis (Hardcover, 3rd ed. 2009)
Stan Z. Li
R4,272 Discovery Miles 42 720 Ships in 10 - 15 working days

Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables us to develop optimal vision algorithms systematically when used with optimization principles. This book presents a comprehensive study on the use of MRFs for solving computer vision problems. Various vision models are presented in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This third edition includes the most recent advances and has new and expanded sections on topics such as: Bayesian Network; Discriminative Random Fields; Strong Random Fields; Spatial-Temporal Models; Learning MRF for Classification. This book is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It is also suitable as a text for advanced courses in these areas.

Multivariate Time Series Analysis in Climate and Environmental Research (Hardcover, 1st ed. 2018): Zhihua Zhang Multivariate Time Series Analysis in Climate and Environmental Research (Hardcover, 1st ed. 2018)
Zhihua Zhang
R4,523 Discovery Miles 45 230 Ships in 10 - 15 working days

This book offers comprehensive information on the theory, models and algorithms involved in state-of-the-art multivariate time series analysis and highlights several of the latest research advances in climate and environmental science. The main topics addressed include Multivariate Time-Frequency Analysis, Artificial Neural Networks, Stochastic Modeling and Optimization, Spectral Analysis, Global Climate Change, Regional Climate Change, Ecosystem and Carbon Cycle, Paleoclimate, and Strategies for Climate Change Mitigation. The self-contained guide will be of great value to researchers and advanced students from a wide range of disciplines: those from Meteorology, Climatology, Oceanography, the Earth Sciences and Environmental Science will be introduced to various advanced tools for analyzing multivariate data, greatly facilitating their research, while those from Applied Mathematics, Statistics, Physics, and the Computer Sciences will learn how to use these multivariate time series analysis tools to approach climate and environmental topics.

Recent Advances in Estimating Nonlinear Models - With Applications in Economics and Finance (Hardcover, 2014 ed.): Jun Ma, Mark... Recent Advances in Estimating Nonlinear Models - With Applications in Economics and Finance (Hardcover, 2014 ed.)
Jun Ma, Mark Wohar
R3,836 R3,396 Discovery Miles 33 960 Save R440 (11%) Ships in 12 - 17 working days

Nonlinear models have been used extensively in the areas of economics and finance. Recent literature on the topic has shown that a large number of series exhibit nonlinear dynamics as opposed to the alternative--linear dynamics. Incorporating these concepts involves deriving and estimating nonlinear time series models, and these have typically taken the form of Threshold Autoregression (TAR) models, Exponential Smooth Transition (ESTAR) models, and Markov Switching (MS) models, among several others. This edited volume provides a timely overview of nonlinear estimation techniques, offering new methods and insights into nonlinear time series analysis. It features cutting-edge research from leading academics in economics, finance, and business management, and will focus on such topics as Zero-Information-Limit-Conditions, using Markov Switching Models to analyze economics series, and how best to distinguish between competing nonlinear models. Principles and techniques in this book will appeal to econometricians, finance professors teaching quantitative finance, researchers, and graduate students interested in learning how to apply advances in nonlinear time series modeling to solve complex problems in economics and finance.

Handbook of  Multilevel Analysis (Hardcover, 2008 ed.): Jan de Leeuw Handbook of Multilevel Analysis (Hardcover, 2008 ed.)
Jan de Leeuw; Foreword by H. Goldstein; Edited by Erik Meijer
R7,613 R4,371 Discovery Miles 43 710 Save R3,242 (43%) Ships in 12 - 17 working days

This book presents the state of the art in multilevel analysis, with an emphasis on more advanced topics. These topics are discussed conceptually, analyzed mathematically, and illustrated by empirical examples. Multilevel analysis is the statistical analysis of hierarchically and non-hierarchically nested data. The simplest example is clustered data, such as a sample of students clustered within schools. Multilevel data are especially prevalent in the social and behavioral sciences and in the biomedical sciences. The chapter authors are all leading experts in the field. Given the omnipresence of multilevel data in the social, behavioral, and biomedical sciences, this book is essential for empirical researchers in these fields.

First Course in Probability, A, Global Edition (Paperback, 10th edition): Sheldon Ross First Course in Probability, A, Global Edition (Paperback, 10th edition)
Sheldon Ross
R2,030 Discovery Miles 20 300 Ships in 12 - 17 working days

For upper-level to graduate courses in Probability or Probability and Statistics, for majors in mathematics, statistics, engineering, and the sciences. Explores both the mathematics and the many potential applications of probability theory A First Course in Probability offers an elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences. Through clear and intuitive explanations, it attempts to present not only the mathematics of probability theory, but also the many diverse possible applications of this subject through numerous examples. The 10th Edition includes many new and updated problems, exercises, and text material chosen both for inherent interest and for use in building student intuition about probability.

Introduction to Modeling and Analysis of Stochastic Systems (Hardcover, 2nd ed. 2011): V.G. Kulkarni Introduction to Modeling and Analysis of Stochastic Systems (Hardcover, 2nd ed. 2011)
V.G. Kulkarni
R4,008 Discovery Miles 40 080 Ships in 12 - 17 working days

This book provides a self-contained review of all the relevant topics in probability theory. A software package called MAXIM, which runs on MATLAB, is made available for downloading. Vidyadhar G. Kulkarni is Professor of Operations Research at the University of North Carolina at Chapel Hill.

Elements of Large-Sample Theory (Hardcover, 1st ed. 1999. Corr. 3rd printing 2004): E. L Lehmann Elements of Large-Sample Theory (Hardcover, 1st ed. 1999. Corr. 3rd printing 2004)
E. L Lehmann
R3,763 Discovery Miles 37 630 Ships in 12 - 17 working days

Elements of Large Sample Theory provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology written at an elementary level. The book is suitable for students at the Master's level in statistics and in aplied fields who have a background of two years of calculus. E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago. Also available: E.L. Lehmann and George Casella, Theory at Point Estimation, Second Edition. Springer-Verlag New York, Inc., 1998, 640 pp., Cloth, ISBN 0-387-98502-6. E.L. Lehmann, Testing Statistical Hypotheses, Second Edition. Springer-Verlag New York, Inc., 1997, 624 pp., Cloth, ISBN 0-387-94919-4.

Uncertainty Theory (Hardcover, 4th ed. 2015): Baoding Liu Uncertainty Theory (Hardcover, 4th ed. 2015)
Baoding Liu
R4,897 R3,612 Discovery Miles 36 120 Save R1,285 (26%) Ships in 12 - 17 working days

When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case. In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees. This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, control, and finance.

Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2016, Stanford, CA, August 14-19 (Hardcover, 1st ed. 2018): Art B. Owen,... Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2016, Stanford, CA, August 14-19 (Hardcover, 1st ed. 2018)
Art B. Owen, Peter W. Glynn
R2,876 Discovery Miles 28 760 Ships in 10 - 15 working days

This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.

Mathematical Reliability: An Expository Perspective (Hardcover, 2004 ed.): R. Soyer, T.A. Mazzuchi, N.D. Singpurwalla Mathematical Reliability: An Expository Perspective (Hardcover, 2004 ed.)
R. Soyer, T.A. Mazzuchi, N.D. Singpurwalla
R2,994 Discovery Miles 29 940 Ships in 10 - 15 working days

In this volume consideration was given to more advanced theoretical approaches and novel applications of reliability to ensure that topics having a futuristic impact were specifically included. Topics like finance, forensics, information, and orthopedics, as well as the more traditional reliability topics were purposefully undertaken to make this collection different from the existing books in reliability. The entries have been categorized into seven parts, each emphasizing a theme that seems poised for the future development of reliability as an academic discipline with relevance. The seven parts are networks and systems; recurrent events; information and design; failure rate function and burn-in; software reliability and random environments; reliability in composites and orthopedics, and reliability in finance and forensics. Embedded within the above are some of the other currently active topics such as causality, cascading, exchangeability, expert testimony, hierarchical modeling, optimization and survival analysis. These topics, when linked with utility theory, constitute the science base of risk analysis.

Generalized Mathieu Series (Hardcover, 1st ed. 2021): Zivorad Tomovski, Delco Leskovski, Stefan Gerhold Generalized Mathieu Series (Hardcover, 1st ed. 2021)
Zivorad Tomovski, Delco Leskovski, Stefan Gerhold
R3,505 Discovery Miles 35 050 Ships in 10 - 15 working days

The Mathieu series is a functional series introduced by Emile Leonard Mathieu for the purposes of his research on the elasticity of solid bodies. Bounds for this series are needed for solving biharmonic equations in a rectangular domain. In addition to Tomovski and his coauthors, Pogany, Cerone, H. M. Srivastava, J. Choi, etc. are some of the known authors who published results concerning the Mathieu series, its generalizations and their alternating variants. Applications of these results are given in classical, harmonic and numerical analysis, analytical number theory, special functions, mathematical physics, probability, quantum field theory, quantum physics, etc. Integral representations, analytical inequalities, asymptotic expansions and behaviors of some classes of Mathieu series are presented in this book. A systematic study of probability density functions and probability distributions associated with the Mathieu series, its generalizations and Planck's distribution is also presented. The book is addressed at graduate and PhD students and researchers in mathematics and physics who are interested in special functions, inequalities and probability distributions.

Stochastic Differential Equations and Processes - SAAP, Tunisia, October 7-9, 2010 (Hardcover, 2012 ed.): Mounir Zili, Darya V.... Stochastic Differential Equations and Processes - SAAP, Tunisia, October 7-9, 2010 (Hardcover, 2012 ed.)
Mounir Zili, Darya V. Filatova
R2,814 Discovery Miles 28 140 Ships in 10 - 15 working days

Selected papers submitted by participants of the international Conference "Stochastic Analysis and Applied Probability 2010" ( www.saap2010.org ) make up the basis of this volume.

The SAAP 2010 was held in Tunisia, from 7-9 October, 2010, and was organized by the "Applied Mathematics & Mathematical Physics" research unit of the preparatory institute to the military academies of Sousse (Tunisia), chaired by Mounir Zili.

The papers cover theoretical, numerical and applied aspects of stochastic processes and stochastic differential equations. The study of such topic is motivated in part by the need to model, understand, forecast and control the behavior of many natural phenomena that evolve in time in a random way. Such phenomena appear in the fields of finance, telecommunications, economics, biology, geology, demography, physics, chemistry, signal processing and modern control theory, to mention just a few.

As this book emphasizes the importance of numerical and theoretical studies of the stochastic differential equations and stochastic processes, it will be useful for a wide spectrum of researchers in applied probability, stochastic numerical and theoretical analysis and statistics, as well as for graduate students.

To make it more complete and accessible for graduate students, practitioners and researchers, the editors Mounir Zili and Daria Filatova have included a survey dedicated to the basic concepts of numerical analysis of the stochastic differential equations, written by Henri Schurz.

Essential Mathematics and Statistics for Forensic Science (Hardcover, New): CD Adam Essential Mathematics and Statistics for Forensic Science (Hardcover, New)
CD Adam
R2,994 R2,597 Discovery Miles 25 970 Save R397 (13%) Out of stock

This text is an accessible, student-friendly introduction to the wide range of mathematical and statistical tools needed by the forensic scientist in the analysis, interpretation and presentation of experimental measurements.

From a basis of high school mathematics, the book develops essential quantitative analysis techniques within the context of a broad range of forensic applications. This clearly structured text focuses on developing core mathematical skills together with an understanding of the calculations associated with the analysis of experimental work, including an emphasis on the use of graphs and the evaluation of uncertainties. Through a broad study of probability and statistics, the reader is led ultimately to the use of Bayesian approaches to the evaluation of evidence within the court. In every section, forensic applications such as ballistics trajectories, post-mortem cooling, aspects of forensic pharmacokinetics, the matching of glass evidence, the formation of bloodstains and the interpretation of DNA profiles are discussed and examples of calculations are worked through. In every chapter there are numerous self-assessment problems to aid student learning.

Its broad scope and forensically focused coverage make this book an essential text for students embarking on any degree course in forensic science or forensic analysis, as well as an invaluable reference for post-graduate students and forensic professionals.

Key features: Offers a unique mix of mathematics and statistics topics, specifically tailored to a forensic science undergraduate degree.All topics illustrated with examples from the forensic science discipline.Written in an accessible, student-friendly way to engage interest and enhance learning and confidence.Assumes only a basic high-school level prior mathematical knowledge.

ANOVA and Mixed Models - A Short Introduction Using R (Hardcover): Lukas Meier ANOVA and Mixed Models - A Short Introduction Using R (Hardcover)
Lukas Meier
R3,844 R3,191 Discovery Miles 31 910 Save R653 (17%) Ships in 9 - 15 working days

Features Accessible to readers with a basic background in probability and statistics Covers fundamental concepts of experimental design and cause-effect relationships Introduces classical ANOVA models, including contrasts and multiple testing Provides an example-based introduction to mixed models Features basic concepts of split-plot and incomplete block designs R code available for all steps Supplementary website with additional resources and updates

Data Science and SDGs - Challenges, Opportunities and Realities (Hardcover, 1st ed. 2021): Bikas Kumar Sinha, Md. Nurul Haque... Data Science and SDGs - Challenges, Opportunities and Realities (Hardcover, 1st ed. 2021)
Bikas Kumar Sinha, Md. Nurul Haque Mollah
R4,581 Discovery Miles 45 810 Ships in 12 - 17 working days

The book presents contributions on statistical models and methods applied, for both data science and SDGs, in one place. Measuring and controlling data of SDGs, data driven measurement of progress needs to be distributed to stakeholders. In this situation, the techniques used in data science, specially, in the big data analytics, play an important role rather than the traditional data gathering and manipulation techniques. This book fills this space through its twenty contributions. The contributions have been selected from those presented during the 7th International Conference on Data Science and Sustainable Development Goals organized by the Department of Statistics, University of Rajshahi, Bangladesh; and cover topics mainly on SDGs, bioinformatics, public health, medical informatics, environmental statistics, data science and machine learning. The contents of the volume would be useful to policymakers, researchers, government entities, civil society, and nonprofit organizations for monitoring and accelerating the progress of SDGs.

Mathematical Statistics (Hardcover, 2nd ed. 2003. Corr. 4th printing 2007): Jun Shao Mathematical Statistics (Hardcover, 2nd ed. 2003. Corr. 4th printing 2007)
Jun Shao
R4,715 Discovery Miles 47 150 Ships in 12 - 17 working days

This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are usefulin statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results. In addition to the classical results that are typically covered in a textbook of a similar level, this book introduces some topics in modern statistical theory that have been developed in recent years, such as Markov chain Monte Carlo, quasi-likelihoods, empirical likelihoods, statistical functionals, generalized estimation equations, the jackknife, and the bootstrap. Jun Shao is Professor of Statistics at the University of Wisconsin, Madison. Also available: Jun Shao and Dongsheng Tu, The Jackknife and Bootstrap, Springer- Verlag New York, Inc., 1995, Cloth, 536 pp., 0-387-94515-6.

An R and S-Plus (R) Companion to Multivariate Analysis (Hardcover, 1st ed. 2005. Corr. 2nd printing 2007): Brian S. Everitt An R and S-Plus (R) Companion to Multivariate Analysis (Hardcover, 1st ed. 2005. Corr. 2nd printing 2007)
Brian S. Everitt
R2,547 Discovery Miles 25 470 Ships in 12 - 17 working days

Most data sets collected by researchers are multivariate, and in the majority of cases the variables need to be examined simultaneously to get the most informative results. This requires the use of one or other of the many methods of multivariate analysis, and the use of a suitable software package such as S-PLUS or R.

In this book the core multivariate methodology is covered along with some basic theory for each method described. The necessary R and S-PLUS code is given for each analysis in the book, with any differences between the two highlighted. A website with all the datasets and code used in the book can be found at http: //biostatistics.iop.kcl.ac.uk/publications/everitt/.

Graduate students, and advanced undergraduates on applied statistics courses, especially those in the social sciences, will find this book invaluable in their work, and it will also be useful to researchers outside of statistics who need to deal with the complexities of multivariate data in their work.

Brian Everitt is Emeritus Professor of Statistics, Kinga (TM)s College, London.

Stochastic and Infinite Dimensional Analysis (Hardcover, 1st ed. 2016): Christopher C. Bernido, Maria Victoria Carpio-Bernido,... Stochastic and Infinite Dimensional Analysis (Hardcover, 1st ed. 2016)
Christopher C. Bernido, Maria Victoria Carpio-Bernido, Martin Grothaus, Tobias Kuna, Maria Joao Oliveira, …
R3,831 R3,392 Discovery Miles 33 920 Save R439 (11%) Ships in 12 - 17 working days

This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit's 75th birthday and celebrate his pioneering and ongoing work in these fields.

Nonstationarities in Hydrologic and Environmental Time Series (Hardcover, 2003 ed.): A.R. Rao, K.H. Hamed, Huey-Long Chen Nonstationarities in Hydrologic and Environmental Time Series (Hardcover, 2003 ed.)
A.R. Rao, K.H. Hamed, Huey-Long Chen
R4,286 Discovery Miles 42 860 Ships in 12 - 17 working days

Most of the time series analysis methods applied today rely heavily on the key assumptions of linearity, Gaussianity and stationarity. Natural time series, including hydrologic, climatic and environmental time series, which satisfy these assumptions seem to be the exception rather than the rule. Nevertheless, most time series analysis is performed using standard methods after relaxing the required conditions one way or another, in the hope that the departure from these assumptions is not large enough to affect the result of the analysis. A large amount of data is available today after almost a century of intensive data collection of various natural time series. In addition to a few older data series such as sunspot numbers, sea surface temperatures, etc., data obtained through dating techniques (tree-ring data, ice core data, geological and marine deposits, etc.), are available. With the advent of powerful computers, the use of simplified methods can no longer be justified, especially with the success of these methods in explaining the inherent variability in natural time series. This book presents a number of new techniques that have been discussed in the literature during the last two decades concerning the investigation of stationarity, linearity and Gaussianity of hydrologic and environmental times series. These techniques cover different approaches for assessing nonstationarity, ranging from time domain analysis, to frequency domain analysis, to the combined time-frequency and time-scale analyses, to segmentation analysis, in addition to formal statistical tests of linearity and Gaussianity. It is hoped that this endeavor would facilitate further research into this important area.

Stochastic Integration in Banach Spaces - Theory and Applications (Hardcover, 2015 ed.): Vidyadhar Mandrekar, Barbara Rudiger Stochastic Integration in Banach Spaces - Theory and Applications (Hardcover, 2015 ed.)
Vidyadhar Mandrekar, Barbara Rudiger
R2,742 R1,688 Discovery Miles 16 880 Save R1,054 (38%) Ships in 12 - 17 working days

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups.

Elements of Computational Statistics (Hardcover, 1st. ed. 2002. Corr. 2nd printing 2005): James E. Gentle Elements of Computational Statistics (Hardcover, 1st. ed. 2002. Corr. 2nd printing 2005)
James E. Gentle
R4,356 Discovery Miles 43 560 Ships in 12 - 17 working days

Computationally intensive methods have become widely used both for statistical inference and for exploratory analyses of data. The methods of computational statistics involve resampling, partitioning, and multiple transformations of a dataset. They may also make use of randomly generated artificial data. Implementation of these methods often requires advanced techniques in numerical analysis, so there is a close connection between computational statistics and statistical computing. This book describes techniques used in computational statistics, and addresses some areas of application of computationally intensive methods, such as density estimation, identification of structure in data, and model building. Although methods of statistical computing are not emphasized in this book, numerical techniques for transformations, for function approximation, and for optimization are explained in the context of the statistical methods. The book includes exercises, some with solutions. The book can be used as a text or supplementary text for various courses in modern statistics at the advanced undergraduate or graduate level, and it can also be used as a reference for statisticians who use computationally-intensive methods of analysis. Although some familiarity with probability and statistics is assumed, the book reviews basic methods of inference, and so is largely self-contained. James Gentle is University Professor of Computational Statistics at George Mason University. He is a Fellow of the American Statistical Association and a member of the International Statistical Institute. He has held several national offices in the American Statistical Association and has served as associate editor for journals of the ASA as well as for other journals in statistics and computing. He is the author of Random Number Generation and Monte Carlo Methods and Numerical Linear Algebra for Statistical Applications.

Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151 (Hardcover, 151st edition): Nikolaos Galatos,... Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151 (Hardcover, 151st edition)
Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski, Hiroakira Ono
R3,983 Discovery Miles 39 830 Ships in 10 - 15 working days

The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics.
As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones.
Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.
- Considers both the algebraic and logical perspective within a common framework.
- Written by experts in the area.
- Easily accessible to graduate students and researchers from other fields.
- Results summarized in tables and diagrams to provide an overview of the area.
- Useful as a textbook for a course in algebraic logic, with exercises and suggested research directions.
- Provides a concise introduction to the subject and leads directly to research topics.
- The ideas from algebra and logic are developed hand-in-hand and the connections are shown in every level.

Diverse Applications of Principal Component Analysis (Hardcover): Rebecca Cross Diverse Applications of Principal Component Analysis (Hardcover)
Rebecca Cross
R2,056 Discovery Miles 20 560 Ships in 12 - 17 working days
Heavy-Tailed Distributions in Disaster Analysis (Hardcover, 2010 Ed.): V Pisarenko, M Rodkin Heavy-Tailed Distributions in Disaster Analysis (Hardcover, 2010 Ed.)
V Pisarenko, M Rodkin
R2,902 Discovery Miles 29 020 Ships in 10 - 15 working days

Mathematically, natural disasters of all types are characterized by heavy tailed distributions. The analysis of such distributions with common methods, such as averages and dispersions, can therefore lead to erroneous conclusions. The statistical methods described in this book avoid such pitfalls. Seismic disasters are studied, primarily thanks to the availability of an ample statistical database. New approaches are presented to seismic risk estimation and forecasting the damage caused by earthquakes, ranging from typical, moderate events to very rare, extreme disasters. Analysis of these latter events is based on the limit theorems of probability and the duality of the generalized Pareto distribution and generalized extreme value distribution. It is shown that the parameter most widely used to estimate seismic risk - Mmax, the maximum possible earthquake value - is potentially non-robust. Robust analogues of this parameter are suggested and calculated for some seismic catalogues. Trends in the costs inferred by damage from natural disasters as related to changing social and economic situations are examined for different regions.

The results obtained argue for sustainable development, whereas entirely different, incorrect conclusions can be drawn if the specific properties of the heavy-tailed distribution and change in completeness of data on natural hazards are neglected.

This pioneering work is directed at risk assessment specialists in general, seismologists, administrators and all those interested in natural disasters and their impact on society.

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