Introduction to Bayesian Statistics

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clust

INTRODUCES THE FUNDAMENTALS OF PROBABILITY, STATISTICS, DECISION THEORY, AND GAME THEORY, AND FEATURES INTERESTING EXAMPLES OF GAMES OF CHANCE AND STRATEGY TO MOTIVATE AND ILLUSTRATE ABSTRACT MATHEMAT

This bundle includes Bora Pajo's Introduction to Research Methods and Ryan J. Winter's A Crash Course in Statistics

NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value; this format costs significantly

This manual contains completely worked-out solutions for all the odd-numbered exercises in the text.

Many professional, high-quality surveys collect data on people's behaviour, experiences, lifestyles and attitudes. The data they produce is more accessible than ever before. This book provides student

Many professional, high-quality surveys collect data on people's behaviour, experiences, lifestyles and attitudes. The data they produce is more accessible than ever before. This book provides student

Reviews fundamental concepts and applications of probability and statistics. After a general overview, it considers special types of random variables, using examples which illustrate their wide variet

Praise for the First Edition"This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of g

?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 o

In a world in which we are constantly surrounded by data, figures, and statistics, it is imperative to understand and to be able to use quantitative methods. Statistical models and methods are among t

Since the 1970s social scientists and scientists in a variety of fields - psychology, sociology, education, psychiatry, economics and engineering - have been interested in problems that require the statistical analysis of data over time and there has been in effect a conceptual revolution in ways of thinking about pattern and regularity. This book is a comprehensive introduction to all the major time-series techniques, both time-domain and frequency-domain. It includes work on linear models that simplify the solution of univariate and multivariate problems. The author begins with a non-mathematical overview: throughout, he provides easy-to-understand, fully worked examples drawn from real studies in psychology and sociology. Other, less comprehensive, books on time-series analysis require calculus: this presupposes only a standard introductory statistics course covering analysis of variance and regression. The chapters are short, designed to build concepts (and the reader's confidence)

An introduction to statistics covers the concepts measurement theory, descriptive statistics, knowlege reprensentation, probability theory, correlations, and parametric statistics.

With its focus on data analysis, statistical reasoning, and the way statisticians actually work, "Introduction to the Practice of Statistics" has helped to revolutionize the way statistics are taught

Computer software is an essential tool for many statistical modelling and data analysis techniques, aiding in the implementation of large data sets in order to obtain useful results. R is one of the

Computer software is an essential tool for many statistical modelling and data analysis techniques, aiding in the implementation of large data sets in order to obtain useful results. R is one of the m

The second edition of a well-received book that was published 24 years ago and continues to sell to this day, An Introduction to Probability and Statistics is now revised to incorporate new informatio

This enthusiastic introduction to the fundamentals of information theory builds from classical Shannon theory through to modern applications in statistical learning. Includes over 210 student exercises, emphasising practical applications in statistics, machine learning and modern communication theory. Accompanied by online instructor solutions.

An approachable introduction to elementary sheaf theory and its applications beyond pure math.Sheaves are mathematical constructions concerned with passages from local properties to global ones. They have played a fundamental role in the development of many areas of modern mathematics, yet the broad conceptual power of sheaf theory and its wide applicability to areas beyond pure math have only recently begun to be appreciated. Taking an applied category theory perspective, Sheaf Theory through Examples provides an approachable introduction to elementary sheaf theory and examines applications including n-colorings of graphs, satellite data, chess problems, Bayesian networks, self-similar groups, musical performance, complexes, and much more. With an emphasis on developing the theory via a wealth of well-motivated and vividly illustrated examples, Sheaf Theory through Examples supplements the formal development of concepts with philosophical reflections on topology, category theory, and

Probabilistic numerical computation formalises the connection between machine learning and applied mathematics. Numerical algorithms approximate intractable quantities from computable ones. They estimate integrals from evaluations of the integrand, or the path of a dynamical system described by differential equations from evaluations of the vector field. In other words, they infer a latent quantity from data. This book shows that it is thus formally possible to think of computational routines as learning machines, and to use the notion of Bayesian inference to build more flexible, efficient, or customised algorithms for computation. The text caters for Masters' and PhD students, as well as postgraduate researchers in artificial intelligence, computer science, statistics, and applied mathematics. Extensive background material is provided along with a wealth of figures, worked examples, and exercises (with solutions) to develop intuition.

Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this e

A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory.This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation. Probabilistic Machine Learning grew out of the author’s 2012 book, Machine Learning: A Probabilistic Perspective. More than just a simple update, this is a completely new book that reflects the dramatic developments in the field since 2012, most notably deep learning. In addition, the ne

A comprehensive introduction to the most commonly used statistical methods relevant in atmospheric, oceanic and climate sciences. Each method is described step-by-step using plain language, and illustrated with concrete examples, with relevant statistical and scientific concepts explained as needed. Particular attention is paid to nuances and pitfalls, with sufficient detail to enable the reader to write relevant code. Topics covered include hypothesis testing, time series analysis, linear regression, data assimilation, extreme value analysis, Principal Component Analysis, Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. The specific statistical challenges that arise in climate applications are also discussed, including model selection problems associated with Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. Requiring no previous background in statistics, this is a highly accessibl

A concise introduction to geophysical data processing - many of the techniques associated with the general field of time series analysis - for advanced students, researchers, and professionals. The textbook begins with calculus before transitioning to discrete time series via the sampling theorem, aliasing, use of complex sinusoids, development of the discrete Fourier transform from the Fourier series, and an overview of linear digital filter types and descriptions. Aimed at senior undergraduate and graduate students in geophysics, environmental science, and engineering with no previous background in linear algebra, probability, or statistics, this textbook draws scenarios and datasets from across the world of geophysics, and shows how data processing techniques can be applied to real-world problems using detailed examples, illustrations, and exercises (using MATLAB or similar computing environment). Online supplementary resources include datasets for students, and a solutions manual a

Light scattering is one of the most well-studied phenomena in nature. It occupies a central place in optical physics, and plays a key role in multiple fields of science and engineering. This volume presents a comprehensive introduction to the subject. For the first time, the authors bring together in a self-contained and systematic manner, the physical concepts and mathematical tools that are used in the modern theory of light scattering and transport, presenting them in a clear, accessible style. The power of these tools is demonstrated by a framework that links various aspects of the subject: scattering theory to radiative transport, radiative transport to diffusion, and field correlations to the statistics of speckle patterns. For graduate students and researchers in optical physics and optical engineering, this book is an invaluable resource on the interaction of light with complex media and the theory of light scattering in disordered and complex systems.

Topological Phases of Matter are an exceptionally dynamic field of research: several of the most exciting recent experimental discoveries and conceptual advances in modern physics have originated in this field. These have generated new, topological, notions of order, interactions and excitations. This text provides an accessible, unified and comprehensive introduction to the phenomena surrounding topological matter, with detailed expositions of the underlying theoretical tools and conceptual framework, alongside accounts of the central experimental breakthroughs. Among the systems covered are topological insulators, magnets, semimetals, and superconductors. The emergence of new particles with remarkable properties such as fractional charge and statistics is discussed alongside possible applications such as fault-tolerant topological quantum computing. Suitable as a textbook for graduate or advanced undergraduate students, or as a reference for more experienced researchers, the book ass

This book addresses the role of statistics and probability in the evaluation of forensic evidence, including both theoretical issues and applications in legal contexts. It discusses what evidence is and how it can be quantified, how it should be understood, and how it is applied (and, sometimes, misapplied). After laying out their philosophical position, the authors begin with a detailed study of the likelihood ratio. Following this grounding, they discuss applications of the likelihood ratio to forensic questions, in the abstract and in concrete cases. The analysis of DNA evidence in particular is treated in great detail. Later chapters concern Bayesian networks, frequentist approaches to evidence, the use of belief functions, and the thorny subject of database searches and familial searching. Finally, the authors provide commentary on various recommendation reports for forensic science. Written to be accessible to a wide audience of applied mathematicians, forensic scientists, and sc

This book addresses the role of statistics and probability in the evaluation of forensic evidence, including both theoretical issues and applications in legal contexts. It discusses what evidence is and how it can be quantified, how it should be understood, and how it is applied (and, sometimes, misapplied). After laying out their philosophical position, the authors begin with a detailed study of the likelihood ratio. Following this grounding, they discuss applications of the likelihood ratio to forensic questions, in the abstract and in concrete cases. The analysis of DNA evidence in particular is treated in great detail. Later chapters concern Bayesian networks, frequentist approaches to evidence, the use of belief functions, and the thorny subject of database searches and familial searching. Finally, the authors provide commentary on various recommendation reports for forensic science. Written to be accessible to a wide audience of applied mathematicians, forensic scientists, and sc

Network thinking and network analysis are rapidly expanding features of ecological research. Network analysis of ecological systems include representations and modelling of the interactions in an ecosystem, in which species or factors are joined by pairwise connections. This book provides an overview of ecological network analysis including generating processes, the relationship between structure and dynamic function, and statistics and models for these networks. Starting with a general introduction to the composition of networks and their characteristics, it includes details on such topics as measures of network complexity, applications of spectral graph theory, how best to include indirect species interactions, and multilayer, multiplex and multilevel networks. Graduate students and researchers who want to develop and understand ecological networks in their research will find this volume inspiring and helpful. Detailed guidance to those already working in network ecology but looking

Network thinking and network analysis are rapidly expanding features of ecological research. Network analysis of ecological systems include representations and modelling of the interactions in an ecosystem, in which species or factors are joined by pairwise connections. This book provides an overview of ecological network analysis including generating processes, the relationship between structure and dynamic function, and statistics and models for these networks. Starting with a general introduction to the composition of networks and their characteristics, it includes details on such topics as measures of network complexity, applications of spectral graph theory, how best to include indirect species interactions, and multilayer, multiplex and multilevel networks. Graduate students and researchers who want to develop and understand ecological networks in their research will find this volume inspiring and helpful. Detailed guidance to those already working in network ecology but looking

Covering both quantitative and qualitative methods, this book examines the breadth of modern market research methods for upper level students across business schools and social science faculties. Modern and trending topics including social networks, machine learning, big data, and artificial intelligence are addressed and real world examples and case studies illustrate the application of the methods. This text examines potential problems, such as researcher bias, and discusses effective solutions in the preparation of research reports and papers, and oral presentations. Assuming no prior knowledge of statistics or econometrics, discrete chapters offer a clear introduction to both, opening up the quantitative methods to all students. Each chapter contains rigorous academic theory, including a synthesis of the recent literature as well as key historical references, applied contextualization and recent research results, making it an excellent resource for practitioners. Online resources i

Covering both quantitative and qualitative methods, this book examines the breadth of modern market research methods for upper level students across business schools and social science faculties. Modern and trending topics including social networks, machine learning, big data, and artificial intelligence are addressed and real world examples and case studies illustrate the application of the methods. This text examines potential problems, such as researcher bias, and discusses effective solutions in the preparation of research reports and papers, and oral presentations. Assuming no prior knowledge of statistics or econometrics, discrete chapters offer a clear introduction to both, opening up the quantitative methods to all students. Each chapter contains rigorous academic theory, including a synthesis of the recent literature as well as key historical references, applied contextualization and recent research results, making it an excellent resource for practitioners. Online resources i