Introduction to Bayesian Statistics

A solid introduction to mathematical modeling for a range of chemical engineering applications, covering model formulation, simplification and validation. It explains how to describe a physical/chemical reality in mathematical language and how to select the type and degree of sophistication for a model. Model reduction and approximation methods are presented, including dimensional analysis, time constant analysis and asymptotic methods. An overview of solution methods for typical classes of models is given. As final steps in model building, parameter estimation and model validation and assessment are discussed. The reader is given hands-on experience of formulating new models, reducing the models and validating the models. The authors assume the knowledge of basic chemical engineering, in particular transport phenomena, as well as basic mathematics, statistics and programming. The accompanying problems, tutorials, and projects include model formulation at different levels, analysis, pa

Originating from the authors' own graduate course at the University of North Carolina, this material has been thoroughly tried and tested over many years, making the book perfect for a two-term course or for self-study. It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue integration, limit theorems in probability, martingales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercises provided. The book is especially useful for graduate students in statistics and related fields of application (biostatistics, econometrics, finance, meteorology, machine learning, and so on) who want to shore up their mathematical foundation. The authors establish common ground for students of varied interests which will serve as a firm 'take-off point' for them as they specialize in areas that exploit mathematical machinery.

Originating from the authors' own graduate course at the University of North Carolina, this material has been thoroughly tried and tested over many years, making the book perfect for a two-term course or for self-study. It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue integration, limit theorems in probability, martingales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercises provided. The book is especially useful for graduate students in statistics and related fields of application (biostatistics, econometrics, finance, meteorology, machine learning, and so on) who want to shore up their mathematical foundation. The authors establish common ground for students of varied interests which will serve as a firm 'take-off point' for them as they specialize in areas that exploit mathematical machinery.

Statistics: Principles and Methods, 7th Edition provides a comprehensive, accurate introduction to statistics for business professionals who need to learn how to apply key concepts. The chapters inclu

Adopting a balanced mix of theory, algorithms and practical design issues, this comprehensive volume explores cutting-edge applications in adaptive wireless communications and the implications these techniques have for future wireless network performance. Presenting practical concerns in the context of different strands from information theory, parameter estimation theory, array processing and wireless communication, the authors present a complete picture of the field. Topics covered include advanced multiple-antenna adaptive processing, ad hoc networking, MIMO, MAC protocols, space-time coding, cellular networks and cognitive radio, with the significance and effects of both internal and external interference a recurrent theme throughout. A broad, self-contained technical introduction to all the necessary mathematics, statistics, estimation theory and information theory is included, and topics are accompanied by a range of engaging end-of-chapter problems. With solutions available onli

Data analysis lies at the heart of every experimental science. Providing a modern introduction to statistics, this book is ideal for undergraduates in physics. It introduces the necessary tools required to analyse data from experiments across a range of areas, making it a valuable resource for students. In addition to covering the basic topics, the book also takes in advanced and modern subjects, such as neural networks, decision trees, fitting techniques and issues concerning limit or interval setting. Worked examples and case studies illustrate the techniques presented, and end-of-chapter exercises help test the reader's understanding of the material.

Data analysis lies at the heart of every experimental science. Providing a modern introduction to statistics, this book is ideal for undergraduates in physics. It introduces the necessary tools required to analyse data from experiments across a range of areas, making it a valuable resource for students. In addition to covering the basic topics, the book also takes in advanced and modern subjects, such as neural networks, decision trees, fitting techniques and issues concerning limit or interval setting. Worked examples and case studies illustrate the techniques presented, and end-of-chapter exercises help test the reader's understanding of the material.

A completely revised and updated edition of a much-acclaimed textbook providing a critical introduction to human personality for psychology students. Levels of Personality carefully avoids the traditional 'catalogue of theories' approach. Instead it relates theories to each other within a conceptual framework of different levels of behaviour, moving inwards and downwards from 'surface level' explanations. Analytic case studies then apply these levels of understanding to areas of special interest such as aggression and sexuality. The author adopts a deep analytical and critical approach and questions whether personality theory and research have really addressed important questions, or produced useful answers. This new edition incorporates two new chapters on personality disorders and on personality in the workplace, as well as improved pedagogical features including statistics boxes, assessment boxes, relevant websites and key references for each chapter.

From the very basics to linear models, this book provides a complete introduction to statistics, data analysis, and R for bioinformatics research and applications. It covers ANOVA, cluster analysis, v

A concise introduction to the fundamental concepts of social scientific thinking and research, this classic text makes scientific thinking, research methods, and statistics accessible to undergraduate

A completely revised and updated edition of a much-acclaimed textbook providing a critical introduction to human personality for psychology students. Levels of Personality carefully avoids the traditional 'catalogue of theories' approach. Instead it relates theories to each other within a conceptual framework of different levels of behaviour, moving inwards and downwards from 'surface level' explanations. Analytic case studies then apply these levels of understanding to areas of special interest such as aggression and sexuality. The author adopts a deep analytical and critical approach and questions whether personality theory and research have really addressed important questions, or produced useful answers. This new edition incorporates two new chapters on personality disorders and on personality in the workplace, as well as improved pedagogical features including statistics boxes, assessment boxes, relevant websites and key references for each chapter.

First published in 1961, this book provides information on the methods of treating series of observations, the field covered embraces portions of both statistics and numerical analysis. Originally intended as an introduction to the topic aimed at students and graduates in physics, the types of observation discussed reflect the standard routine work of the time in the physical sciences. The text partly reflects an aim to offer a better balance between theory and practice, reversing the tendency of books on numerical analysis to omit numerical examples illustrating the applications of the methods. This book will be of value to anyone with an interest in the theoretical development of its field.

Stochastic Dynamics of Marine Structures is a text for students and a reference for professionals on the basic theory and methods used for stochastic modelling and analysis of marine structures subjected to environmental loads. The first part of the book provides a detailed introduction to the basic dynamic analysis of structures, serving as a foundation for later chapters on stochastic response analysis. This includes an extensive chapter on the finite element method. A careful introduction to stochastic modelling is provided, which includes such concepts as stochastic process, variance spectrum, random environmental processes, response spectrum, response statistics and short- and long-term extreme value models. The second part of the book offers detailed discussion of limit state design approaches, fatigue design methods, the equations of motion for dynamic structures and numerical solution techniques. The final chapter highlights methods for prediction of extreme values from measure

Providing a fundamental introduction to all aspects of modern plasma chemistry, this book describes mechanisms and kinetics of chemical processes in plasma, plasma statistics, thermodynamics, fluid mechanics and electrodynamics, as well as all major electric discharges applied in plasma chemistry. Fridman considers most of the major applications of plasma chemistry, from electronics to thermal coatings, from treatment of polymers to fuel conversion and hydrogen production and from plasma metallurgy to plasma medicine. It is helpful to engineers, scientists and students interested in plasma physics, plasma chemistry, plasma engineering and combustion, as well as chemical physics, lasers, energy systems and environmental control. The book contains an extensive database on plasma kinetics and thermodynamics and numerical formulas for practical calculations related to specific plasma-chemical processes and applications. Problems and concept questions are provided, helpful in courses relate

?Between Certainty & Uncertainty” is a one-of–a-kind short course on statistics for students, engineers and researchers. It is a fascinating introduction to statistics and probability with notes

Stein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, Breuer–Major theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely self-contained, the book is perfect for self-study. It will appeal to researchers and graduate students in probability and statistics, especially those who wi

Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on compu

By the late nineteenth century, twenty-nine Chinese ports were open for foreign trade. Often run by foreign commissioners and no longer subject to the stringent local laws, these ports levied one of the smallest import taxes in the world, and Chinese commerce therefore exploded. Originally published in 1900, this account by William Barclay Parsons (1859–1932) investigates the ensuing surge of economic and industrial development in the eastern provinces. Including an introduction to China's history and the structure of its civil service, the book analyses the corrupt but ingenious world of customs officials, the importance of American cotton interests, and export statistics which reveal the multimillion-dollar smuggling operations that slipped around official embargoes. Set against a backdrop of electric lights and western labels in even the most closed of cities, this book offers a fascinating glimpse into the early stages of today's global market.

A concise, easily accessible introduction to descriptive and inferential techniquesStatistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers

This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Fréchet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicia

The 'student of clouds' Luke Howard (1772–1864) published this work of statistics on weather conditions in London in two volumes, in 1818 and 1820. Howard was by profession an industrial chemist, but his great interest in meteorology led to his studies on clouds (also reissued in this series), and his devising of the system of Latin cloud names which was adopted internationally and is still in use. Volume 1 begins with an introduction to the work, explaining his intention to make available in one place consistent records of weather events. He argues that for the benefit of 'agriculture and navigation', a systematic approach is required, and he outlines his methods and equipment in some detail. The tables of observations taken at Plaistow, near London, in the years 1806–9 then begin, and are interspersed with notes and a commentary which includes accounts of similar weather phenomena observed elsewhere.

The 'student of clouds' Luke Howard (1772–1864) published this work of statistics on weather conditions in London in two volumes, in 1818 and 1820. Volume 1 begins with an introduction to the work, fo

"Statistical Concepts consists of the last 9 chapters of An Introduction to Statistical Concepts, 3rd ed. Designed for the second course in statistics it is one of the few texts that focuses just on i

Collecting, Managing, and Assessing Data Using Sample Surveys provides a thorough, step-by-step guide to the design and implementation of surveys. Beginning with a primer on basic statistics, the first half of the book takes readers on a comprehensive tour through the basics of survey design. Topics covered include the ethics of surveys, the design of survey procedures, the design of the survey instrument, how to write questions and how to draw representative samples. Having shown readers how to design surveys, the second half of the book discusses a number of issues surrounding their implementation, including repetitive surveys, the economics of surveys, web-based surveys, coding and data entry, data expansion and weighting, the issue of non-response, and the documenting and archiving of survey data. The book is an excellent introduction to the use of surveys for graduate students as well as a useful reference work for scholars and professionals.

Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a val

Collecting, Managing, and Assessing Data Using Sample Surveys provides a thorough, step-by-step guide to the design and implementation of surveys. Beginning with a primer on basic statistics, the first half of the book takes readers on a comprehensive tour through the basics of survey design. Topics covered include the ethics of surveys, the design of survey procedures, the design of the survey instrument, how to write questions and how to draw representative samples. Having shown readers how to design surveys, the second half of the book discusses a number of issues surrounding their implementation, including repetitive surveys, the economics of surveys, web-based surveys, coding and data entry, data expansion and weighting, the issue of non-response, and the documenting and archiving of survey data. The book is an excellent introduction to the use of surveys for graduate students as well as a useful reference work for scholars and professionals.

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.

This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are cover

Kadane (Carnegie Mellon U., Pennsylvania) explains a Bayesian approach to statistics, incorporating the three legs the field stands on: mathematics, computing, and philosophy. Different parts of the t

Quantitative risk assessments cannot eliminate risk, nor can they resolve trade-offs. They can, however, guide principled risk management and reduction - if the quality of assessment is high and decision makers understand how to use it. This book builds a unifying scientific framework for discussing and evaluating the quality of risk assessments and whether they are fit for purpose. Uncertainty is a central topic. In practice, uncertainties about inputs are rarely reflected in assessments, with the result that many safety measures are considered unjustified. Other topics include the meaning of a probability, the use of probability models, the use of Bayesian ideas and techniques, and the use of risk assessment in a practical decision-making context. Written for professionals, as well as graduate students and researchers, the book assumes basic probability, statistics and risk assessment methods. Examples make concepts concrete, and three extended case studies show the scientific framew

A unique introduction to the design, analysis, and presentation of scientific projects, this is an essential textbook for undergraduate majors in science and mathematics. The textbook gives an overview of the main methods used in scientific research, including hypothesis testing, the measurement of functional relationships, and observational research. It describes important features of experimental design, such as the control of errors, instrument calibration, data analysis, laboratory safety, and the treatment of human subjects. Important concepts in statistics are discussed, focusing on standard error, the meaning of p values, and use of elementary statistical tests. The textbook introduces some of the main ideas in mathematical modeling, including order-of-magnitude analysis, function fitting, Fourier transforms, recursion relations, and difference approximations to differential equations. It also provides guidelines on accessing scientific literature, and preparing scientific paper

Now updated for SPSS? Statistics Version 18, DOING DATA ANALYSIS WITH SPSS is an excellent supplement to any introductory statistics course. It provides a practical and useful introduction to SPSS an

This 2006 textbook discusses the fundamentals and applications of statistical thermodynamics for beginning graduate students in the physical and engineering sciences. Building on the prototypical Maxwell–Boltzmann method and maintaining a step-by-step development of the subject, this book assumes the reader has no previous exposure to statistics, quantum mechanics or spectroscopy. The book begins with the essentials of statistical thermodynamics, pauses to recover needed knowledge from quantum mechanics and spectroscopy, and then moves on to applications involving ideal gases, the solid state and radiation. A full introduction to kinetic theory is provided, including its applications to transport phenomena and chemical kinetics. A highlight of the textbook is its discussion of modern applications, such as laser-based diagnostics. The book concludes with a thorough presentation of the ensemble method, featuring its use for real gases. Numerous examples and prompted homework problems enr

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

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances fo

Although both philosophers and scientists are interested in how to obtain reliable knowledge in the face of error, there is a gap between their perspectives that has been an obstacle to progress. By means of a series of exchanges between the editors and leaders from the philosophy of science, statistics and economics, this volume offers a cumulative introduction connecting problems of traditional philosophy of science to problems of inference in statistical and empirical modelling practice. Philosophers of science and scientific practitioners are challenged to reevaluate the assumptions of their own theories - philosophical or methodological. Practitioners may better appreciate the foundational issues around which their questions revolve and thereby become better 'applied philosophers'. Conversely, new avenues emerge for finally solving recalcitrant philosophical problems of induction, explanation and theory testing.

This book provides a clear introduction to this important area of statistics. The author provides a wide of coverage of different kinds of multilevel models, and how to interpret different statistica

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events (risk) and when we lack them (ambiguity). The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering.

This 1971 volume brings together a number of tracts on problems of India's economic development, particularly in relation to the changes taking place in her international trade. The first half of the nineteenth century was a period of important economic transition for India. A vital aspect of it was the rapid expansion in the volume and value of Indian foreign trade, accompanied by fundamental structural changes, which transformed the old eighteenth-century mercantile pattern of India's trade with the West into a system based on an exchange of primary commodities for finished manufactured goods. The papers reprinted here illustrate first the quantitative aspects of Indian trade in this period, and secondly its institutional and policy features. The editor provides a full introduction and tables of statistics.

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events (risk) and when we lack them (ambiguity). The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering.