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Statistical Thermodynamics: Understanding the Properties of Macroscopic Systems
by Lukong Cornelius Fai Gary Matthew WysinPresenting a look at the modern evolution of statistical thermodynamics, this book provides a detailed overview of the statistical principles used to obtain the physical and thermodynamic properties of macroscopic systems. Going further than many advanced textbooks, it includes Bose-Einstein, Fermi-Dirac statistics, and lattice dynamics as well as applications in polaron theory, electronic gas in a magnetic field, thermodynamics of dielectrics, and magnetic materials in a magnetic field. The text also examines statistical thermodynamics using functional integration and Feynman path integrals. In addition, it features physical results and worked problems.
Statistical Tools for Environmental Quality Measurement (Chapman & Hall/CRC Applied Environmental Statistics)
by Douglas E. Splitstone Michael E. GinevanWhen interpreting environmental data, scientists and engineers first must select the correct statistical tool to use for their analysis. By doing this they will be able to make sound decisions in their efforts to solve environmental problems. They need a detailed reference that points out the subtle differences between statistical procedures, makin
Statistical and Computational Methods in Brain Image Analysis (Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series)
by Moo K. ChungThe massive amount of nonstandard high-dimensional brain imaging data being generated is often difficult to analyze using current techniques. This challenge in brain image analysis requires new computational approaches and solutions. But none of the research papers or books in the field describe the quantitative techniques with detailed illustratio
Statistical and Condensed Matter Physics
by Serguei N. BurmistrovThe book outlines the fundamentals of statistical and condensed matter physics. The statistical physics is the basis of condensed matter physics and the tool for studying a variety of condensed media in the thermodynamic (heat) conditions. The statistical physics is presented within the framework of canonical Gibbs distribution entailing the relations known from the classical (heat) thermodynamics. The application of the statistical theory embraces such topics as ideal classical and quantum gases, Bose-type excitations, phase transitions and critical phenomena, normal Fermi liquid, superconductivity, weakly non-ideal Bose gases, superfluidity, and magnetism. Each section ends with one or several problems with the solutions clarifying the paragraph content and delivering some additional physical examples. The problems give an opportunity for a reader to check the own real knowledge of the material studied.
Statistical and Inductive Probabilities (Dover Books on Mathematics)
by Hugues LeblancAmong probability theorists, a bitter controversy has raged for decades between the adherents of John Maynard Keynes' A Treatise on Probability (1921) and those of Richard von Mises' "Grundlagen der Wahrscheinlichkeitsrechnung" (1919). Keynes declared that probabilities measure the extent to which a so-called evidence proposition supports another sentence. Von Mises insisted that they measure the relative frequency with which the members of a so-called reference set belong to another set. Statistical and Inductive Probabilities offers an evenhanded treatment of this issue, asserting that both statistical and inductive probabilities may be treated as sentence-theoretic measurements, and that the latter qualify as estimates of the former.Beginning with a survey of the essentials of sentence theory and of set theory, author Hugues Leblanc examines statistical probabilities (which are allotted to sets by von Mises' followers), showing that statistical probabilities may be passed on to sentences, and thereby qualify as truth-values. Leblanc concludes with an exploration of inductive probabilities (which Keynes' followers allot to sentences), demonstrating their reinterpretation as estimates of truth-values.Each chapter is preceded by a summary of its contents. Illustrations accompany most definitions and theorems, and footnotes elucidate technicalities and bibliographical references.
Statistical and Multivariate Analysis in Material Science
by Giorgio LucianoThe present work is an introductory text in statistics, addressed to researchers and students in the field of material science. It aims to give the readers basic knowledge on how statistical reasoning is exploitable in this field, improving their knowledge of statistical tools and helping them to carry out statistical analyses and to interpret the results. It also focuses on establishing a consistent multivariate workflow starting from a correct design of experiment followed by a multivariate analysis process.
Statistical and Nonlinear Physics (Encyclopedia of Complexity and Systems Science Series)
by Bulbul ChakrabortyThis volume of the Encyclopedia of Complexity and Systems Science, Second Edition, focuses on current challenges in the field from materials and mechanics to applications of statistical and nonlinear physics in the life sciences. Challenges today are mostly in the realm of non-equilibrium systems, although certain equilibrium systems also present serious hurdles. Where possible, pairwise articles focus on a single topic, one from a theoretical perspective and the other from an experimental one, providing valuable insights. In other cases, theorists and experimentalists have collaborated on a single article. Coverage includes both quantum and classical systems, and emphasizes 1) mature fields that are not covered in the current specialist literature, (2) topics that fall through the cracks in disciplinary journals/books, or (3) developing areas where the knowledge base is large and robust and upon which future developments will depend. The result is an invaluable resource for condensed matter physicists, material scientists, engineers and life scientists.
Statistical and Thermal Physics: An Introduction
by Michael J.R. HochThermal and statistical physics has established the principles and procedures needed to understand and explain the properties of systems consisting of macroscopically large numbers of particles. By developing microscopic statistical physics and macroscopic classical thermodynamic descriptions in tandem, Statistical and Thermal Physics: An Introduction provides insight into basic concepts and relationships at an advanced undergraduate level. This second edition is updated throughout, providing a highly detailed, profoundly thorough, and comprehensive introduction to the subject and features exercises within the text as well as end-of-chapter problems. Part I of this book consists of nine chapters, the first three of which deal with the basics of equilibrium thermodynamics, including the fundamental relation. The following three chapters introduce microstates and lead to the Boltzmann definition of the entropy using the microcanonical ensemble approach. In developing the subject, the ideal gas and the ideal spin system are introduced as models for discussion. The laws of thermodynamics are compactly stated. The final three chapters in Part I introduce the thermodynamic potentials and the Maxwell relations. Applications of thermodynamics to gases, condensed matter, and phase transitions and critical phenomena are dealt with in detail. Initial chapters in Part II present the elements of probability theory and establish the thermodynamic equivalence of the three statistical ensembles that are used in determining probabilities. The canonical and the grand canonical distributions are obtained and discussed. Chapters 12-15 are concerned with quantum distributions. By making use of the grand canonical distribution, the Fermi–Dirac and Bose–Einstein quantum distribution functions are derived and then used to explain the properties of ideal Fermi and Bose gases. The Planck distribution is introduced and applied to photons in radiation and to phonons on solids. The last five chapters cover a variety of topics: the ideal gas revisited, nonideal systems, the density matrix, reactions, and irreversible thermodynamics. A flowchart is provided to assist instructors on planning a course. Key Features: Fully updated throughout, with new content on exciting topics, including black hole thermodynamics, Heisenberg antiferromagnetic chains, entropy and information theory, renewable and nonrenewable energy sources, and the mean field theory of antiferromagnetic systems Additional problem exercises with solutions provide further learning opportunities Suitable for advanced undergraduate students in physics or applied physics. Michael J.R. Hoch spent many years as a visiting scientist at the National High Magnetic Field Laboratory at Florida State University, USA. Prior to this, he was a professor of physics and the director of the Condensed Matter Physics Research Unit at the University of the Witwatersrand, Johannesburg, where he is currently professor emeritus in the School of Physics.
Statistical and Thermal Physics: Fundamentals and Applications
by M.D. SturgeThis book is based on many years of teaching statistical and thermal physics. It assumes no previous knowledge of thermodynamics, kinetic theory, or probability---the only prerequisites are an elementary knowledge of classical and modern physics, and of multivariable calculus. The first half of the book introduces the subject inductively but rigorously, proceeding from the concrete and specific to the abstract and general. In clear physical language the book explains the key concepts, such as temperature, heat, entropy, free energy, chemical potential, and distributions, both classical and quantum. The second half of the book applies these concepts to a wide variety of phenomena, including perfect gases, heat engines, and transport processes. Each chapter contains fully worked examples and real-world problems drawn from physics, astronomy, biology, chemistry, electronics, and mechanical engineering.
Statistical and Thermal Physics: With Computer Applications
by Harvey Gould Jan TobochnikThis textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics. Statistical and Thermal Physicsbegins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on thermal physics, this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students. Integrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text Provides self-contained introductions to thermodynamics and statistical mechanics Discusses probability concepts and methods in detail Contains ideas and methods from contemporary research Includes advanced chapters that provide a natural bridge to graduate study Features more than 400 problems Programs are open source and available in an executable cross-platform format Solutions manual (available only to teachers)
Statistics Done Wrong
by Alex ReinhartScientific progress depends on good research, and good research needs good statistics. But statistical analysis is tricky to get right, even for the best and brightest of us. You'd be surprised how many scientists are doing it wrong.Statistics Done Wrong is a pithy, essential guide to statistical blunders in modern science that will show you how to keep your research blunder-free. You'll examine embarrassing errors and omissions in recent research, learn about the misconceptions and scientific politics that allow these mistakes to happen, and begin your quest to reform the way you and your peers do statistics.You'll find advice on:–Asking the right question, designing the right experiment, choosing the right statistical analysis, and sticking to the plan–How to think about p values, significance, insignificance, confidence intervals, and regression–Choosing the right sample size and avoiding false positives–Reporting your analysis and publishing your data and source code–Procedures to follow, precautions to take, and analytical software that can helpScientists: Read this concise, powerful guide to help you produce statistically sound research. Statisticians: Give this book to everyone you know.The first step toward statistics done right is Statistics Done Wrong.
Statistics Explained
by Steve MckillupAn understanding of statistics and experimental design is essential for life science studies, but many students lack a mathematical background and some even dread taking an introductory statistics course. Using a refreshingly clear and encouraging reader-friendly approach, this book helps students understand how to choose, carry out, interpret and report the results of complex statistical analyses, critically evaluate the design of experiments and proceed to more advanced material. Taking a straightforward conceptual approach, it is specifically designed to foster understanding, demystify difficult concepts and encourage the unsure. Even complex topics are explained clearly, using a pictorial approach with a minimum of formulae and terminology. Examples of tests included throughout are kept simple by using small data sets. In addition, end-of-chapter exercises, new to this edition, allow self-testing. Handy diagnostic tables help students choose the right test for their work and remain a useful refresher tool for postgraduates.
Statistics and Analysis of Scientific Data
by Massimiliano BonamenteStatistics and Analysis of Scientific Data covers the foundations of probability theory and statistics, and a number of numerical and analytical methods that are essential for the present-day analyst of scientific data. Topics covered include probability theory, distribution functions of statistics, fits to two-dimensional datasheets and parameter estimation, Monte Carlo methods and Markov chains. Equal attention is paid to the theory and its practical application, and results from classic experiments in various fields are used to illustrate the importance of statistics in the analysis of scientific data. The main pedagogical method is a theory-then-application approach, where emphasis is placed first on a sound understanding of the underlying theory of a topic, which becomes the basis for an efficient and proactive use of the material for practical applications. The level is appropriate for undergraduates and beginning graduate students, and as a reference for the experienced researcher. Basic calculus is used in some of the derivations, and no previous background in probability and statistics is required. The book includes many numerical tables of data, as well as exercises and examples to aid the students' understanding of the topic.
Statistics and Analysis of Scientific Data
by Massimiliano BonamenteThe revised second edition of this textbook provides the reader with a solid foundation in probability theory and statistics as applied to the physical sciences, engineering and related fields. It covers a broad range of numerical and analytical methods that are essential for the correct analysis of scientific data, including probability theory, distribution functions of statistics, fits to two-dimensional data and parameter estimation, Monte Carlo methods and Markov chains. Features new to this edition include: * a discussion of statistical techniques employed in business science, such as multiple regression analysis of multivariate datasets. * a new chapter on the various measures of the mean including logarithmic averages. * new chapters on systematic errors and intrinsic scatter, and on the fitting of data with bivariate errors. * a new case study and additional worked examples. * mathematical derivations and theoretical background material have been appropriately marked, to improve the readability of the text. * end-of-chapter summary boxes, for easy reference. As in the first edition, the main pedagogical method is a theory-then-application approach, where emphasis is placed first on a sound understanding of the underlying theory of a topic, which becomes the basis for an efficient and practical application of the material. The level is appropriate for undergraduates and beginning graduate students, and as a reference for the experienced researcher. Basic calculus is used in some of the derivations, and no previous background in probability and statistics is required. The book includes many numerical tables of data, as well as exercises and examples to aid the readers' understanding of the topic.
Statistics and Data Analysis for Microarrays Using R and Bioconductor (Chapman & Hall/CRC Computational Biology Series)
by Sorin DraghiciRichly illustrated in color, Statistics and Data Analysis for Microarrays Using R and Bioconductor, Second Edition provides a clear and rigorous description of powerful analysis techniques and algorithms for mining and interpreting biological information. Omitting tedious details, heavy formalisms, and cryptic notations, the text takes a hands-on, example-based approach that teaches students the basics of R and microarray technology as well as how to choose and apply the proper data analysis tool to specific problems.New to the Second EditionCompletely updated and double the size of its predecessor, this timely second edition replaces the commercial software with the open source R and Bioconductor environments. Fourteen new chapters cover such topics as the basic mechanisms of the cell, reliability and reproducibility issues in DNA microarrays, basic statistics and linear models in R, experiment design, multiple comparisons, quality control, data pre-processing and normalization, Gene Ontology analysis, pathway analysis, and machine learning techniques. Methods are illustrated with toy examples and real data and the R code for all routines is available on an accompanying downloadable resource.With all the necessary prerequisites included, this best-selling book guides students from very basic notions to advanced analysis techniques in R and Bioconductor. The first half of the text presents an overview of microarrays and the statistical elements that form the building blocks of any data analysis. The second half introduces the techniques most commonly used in the analysis of microarray data.
Statistics and Scaling in Turbulent Rayleigh-Bénard Convection
by Emily S.C. ChingThis Brief addresses two issues of interest of turbulent Rayleigh-Bénard convection. The rst issue is the characterization and understanding of the statistics of the velocity and temperature uctuations in the system. The second issue is the revelation and understanding of the nature of the scaling behavior of the velocity temperature structure functions. The problem under the Oberbeck-Boussinesq approximation is formulated. The statistical tools, including probability density functions (PDF) and conditional statistics, for studying fluctuations are introduced, and implicit PDF formulae for fluctuations obeying certain statistical symmetries are derived. Applications of these PDF formulae to study the fluctuations in turbulent Rayleigh-Bénard convection are then discussed. The phenomenology of the different types of scaling behavior: the Bolgiano-Obhukov scaling behavior when buoyancy effects are significant and the Kolmogorov-Obukhov-Corrsin scaling behavior when they are not, is introduced. A crossover between the two types of scaling behavior is expected to occur at the Bolgiano length scale above which buoyancy is important. The experimental observations are reviewed. In the central region of the convective cell, the Kolmogorov-Obukhov-Corrsin scaling behavior has been observed. On the other hand, the Bolgiano-Obukhov scaling remains elusive only until recently. By studying the dependence of the conditional temperature structure functions on the locally averaged thermal dissipation rate, evidence for the Bolgiano-Obukhov scaling has recently been found near the bottom plate. The different behaviors observed in the two regions could be attributed to the different size of the Bolgiano scale. What physics determines the relative size of the Bolgiano scale remains to be understood. The Brief is concluded by a discussion of these outstanding issues.
Statistics by Simulation: A Synthetic Data Approach
by Aaron M. Ellison Carsten F. DormannAn accessible guide to understanding statistics using simulations, with examples from a range of scientific disciplinesReal-world challenges such as small sample sizes, skewed distributions of data, biased sampling designs, and more predictors than data points are pushing the limits of classical statistical analysis. This textbook provides a new tool for the statistical toolkit: data simulations. It shows that using simulation and data-generating models is an excellent way to validate statistical reasoning and to augment study design and statistical analysis with planning and visualization. Although data simulations are not new to professional statisticians, Statistics by Simulation makes the approach accessible to a broader audience, with examples from many fields. It introduces the reasoning behind data simulation and then shows how to apply it in planning experiments or observational studies, developing analytical workflows, deploying model diagnostics, and developing new indices and statistical methods.• Covers all steps of statistical practice, from planning projects to post-hoc analysis and model checking• Provides examples from disciplines including sociology, psychology, ecology, economics, physics, and medicine• Includes R code for all examples, with data and code freely available online• Offers bullet-point outlines and summaries of each chapter• Minimizes the use of jargon and requires only basic statistical background and skills
Statistics for Biotechnology Process Development
by Harry Yang Todd CoffeyWritten specifically for biotechnology scientists, engineers, and quality professionals, this book describes and demonstrates the proper application of statistical methods throughout Chemistry, Manufacturing, and Controls (CMC). Filled with case studies, examples, and easy-to-follow explanations of how to perform statistics in modern software, it is the first book on CMC statistics written primarily for practitioners. While statisticians will also benefit from this book, it is written particularly for industry professionals who don’t have access to a CMC statistician or who want to be more independent in the design and analysis of their experiments. Provides an introduction to the statistical concepts important in the biotechnology industry Focuses on concepts with theoretical details kept to a minimum Includes lots of real examples and case studies to illustrate the methods Uses JMP software for implementation of the methods Offers a text suitable for scientists in the industry with some quantitative training Written and edited by seasoned veterans of the biotechnology industry, this book will prove useful to a wide variety of biotechnology professionals. The book brings together individual chapters that showcase the use of statistics in the most salient areas of CMC.
Statistics for Chemical and Process Engineers
by Yuri A. W. ShardtA coherent, concise and comprehensive course in the statistics needed for a modern career in chemical engineering; covers all of the concepts required for the American Fundamentals of Engineering examination. This book shows the reader how to develop and test models, design experiments and analyse data in ways easily applicable through readily available software tools like MS Excel® and MATLAB®. Generalized methods that can be applied irrespective of the tool at hand are a key feature of the text. The reader is given a detailed framework for statistical procedures covering: · data visualization; · probability; · linear and nonlinear regression; · experimental design (including factorial and fractional factorial designs); and · dynamic process identification. Main concepts are illustrated with chemical- and process-engineering-relevant examples that can also serve as the bases for checking any subsequent real implementations. Questions are provided (with solutions available for instructors) to confirm the correct use of numerical techniques, and templates for use in MS Excel and MATLAB can also be downloaded from extras. springer. com. With its integrative approach to system identification, regression and statistical theory, Statistics for Chemical and Process Engineers provides an excellent means of revision and self-study for chemical and process engineers working in experimental analysis and design in petrochemicals, ceramics, oil and gas, automotive and similar industries and invaluable instruction to advanced undergraduate and graduate students looking to begin a career in the process industries.
Statistics for Chemical and Process Engineers: A Modern Approach
by Yuri A.W. ShardtA coherent, concise, and comprehensive course in the statistics needed for a modern career in chemical engineering covers all of the concepts required for the American Fundamentals of Engineering Examination.Statistics for Chemical and Process Engineers (second edition) shows the reader how to develop and test models, design experiments and analyze data in ways easily applicable through readily available software tools like MS Excel® and MATLAB® and is updated for the most recent versions of both. Generalized methods that can be applied irrespective of the tool at hand are a key feature of the text, and it now contains an introduction to the use of state-space methods.The reader is given a detailed framework for statistical procedures covering: data visualization;probability;linear and nonlinear regression; experimental design (including factorial and fractional factorial designs); and dynamic process identification. Main concepts are illustrated with chemical- and process-engineering-relevant examples that can also serve as the bases for checking any subsequent real implementations. Questions are provided (with solutions available for instructors) to confirm the correct use of numerical techniques, and templates for use in MS Excel and MATLAB are also available for download. With its integrative approach to system identification, regression, and statistical theory, this book provides an excellent means of revision and self-study for chemical and process engineers working in experimental analysis and design in petrochemicals, ceramics, oil and gas, automotive and similar industries, and invaluable instruction to advanced undergraduate and graduate students looking to begin a career in the process industries.
Statistics for Clinicians
by Andrew OwenThis book provides clinical medicine readers with a detailed explanation of statistical concepts using non-technical terms. This allows clinicians and others without specialist statistical knowledge to understand the medical literature where such concepts are used. Many examples from the medical literature are used to exemplify how these concepts are used in practice. Current books written for clinicians fall into two broad categories. Simple texts that are not designed to cover many important statistical concepts used in the medical literature. Comprehensive texts which cover many statistical principles in detail, including statistical theory, but which are more challenging to read and do not always cover many important statistical techniques used in the medical literature. This book assists in the understanding of these techniques.Statistics for Clinicians covers such topics in a robust non-technical manner accessible to clinicians and is intended for hospital consultants, junior doctors and general practitioners. Undergraduates in biomedical sciences and medicine may also find some sections valuable.
Statistics for Clinicians: How Much Should a Doctor Know?
by Ahmed HassounaHow much statistics does a clinician, surgeon or nurse need to know?This book provides an essential handbook to help appraise evidence in a scientific paper, to design and interpret the results of research correctly, to guide our students and to review the work of our colleagues. This title is written by a clinician exclusively for fellow clinicians, in their own language and not in statistical or epidemiological terms.When clinicians discuss probability, it is focussed on how it applies to the management of patients in the flesh and how they are managed in a clinical setting. Statistics for Clinicians does not overlook the basis of statistics, but reviews techniques specific to medicine with an emphasis on their application. It ensures that readers have the correct tools to hand, including worked examples, guides and links to online calculators and free software, enabling readers to execute most statistical calculations. This book will therefore be enormously helpful for many working across all fields of medicine at any stage of their career.
Statistics for Engineering and the Sciences
by William M. Mendenhall Terry L. SincichPrepare Your Students for Statistical Work in the Real WorldStatistics for Engineering and the Sciences, Sixth Edition is designed for a two-semester introductory course on statistics for students majoring in engineering or any of the physical sciences. This popular text continues to teach students the basic concepts of data description and statist
Statistics for Engineering and the Sciences Student Solutions Manual
by William M. Mendenhall Nancy S. Boudreau Terry L. SincichA companion to Mendenhall and Sincich’s Statistics for Engineering and the Sciences, Sixth Edition, this student resource offers full solutions to all of the odd-numbered exercises.
Statistics for Environmental Science and Management (Chapman & Hall/CRC Applied Environmental Statistics)
by Bryan F.J. ManlyPresenting a nonmathematical approach to this topic, Statistics for Environmental Science and Management introduces frequently used statistical methods and practical applications for the environmental field. This second edition features updated references and examples along with new and expanded material on data quality objectives, the generalized linear model, spatial data analysis, and Monte Carlo risk assessment. Additional topics covered include environmental monitoring, impact assessment, censored data, environmental sampling, the role of statistics in environmental science, assessing site reclamation, and drawing conclusions from data.