Introduction to Bayesian Statistics

Ninety percent of the cells in the human body are bacteria, and humans may be host to many thousands of different species of bacteria. These striking statistics are part of a new paradigm in microbiology in which bacteria are no longer viewed as disease-causing killers but more as lifelong partners which are often essential for the survival of their host. This book brings together a group of diverse scientists - evolutionary biologists, immunologists, molecular biologists, microbiologists, pathologists and mathematicians - to discuss the evolution and mechanisms of bacteria-host interactions at all levels of complexity. Chapters deal with the evolution of these interactions over the last 60 years (since the introduction of antibiotics) to a period of 3.8 billion years (since the evolution of single-celled life) and discuss bacterial interactions with multicellular life forms from coral reefs to humans. Researchers and graduate students across the life sciences will find this book of in

This detailed introduction to distribution theory is designed as a text for the probability portion of the first year statistical theory sequence for Master's and PhD students in statistics, biostatis

Designed for the one-term MBA or undergraduate introduction to business statistics course, this text places emphasis on data and the common techniques and methods used to analyze them in business. It

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

This concise, entry level text provides an introduction to the importance of genetic studies in conservation and presents the essentials of the discipline in an easy-to-follow format, with main points and terms clearly highlighted. The authors assume only a basic knowledge of Mendelian genetics and simple statistics, making the book accessible to those with a limited background in these areas. Connections between conservation genetics and the wider field of conservation biology are interwoven throughout the book. Worked examples are provided throughout to help illustrate key equations and glossary and suggestions for further reading provide additional support for the reader. Many beautiful pen and ink portraits of endangered species are included to enhance the text. Written for short, introductory level courses in genetics, conservation genetics and conservation biology, this book will also be suitable for practising conservation biologists, zoo biologists and wildlife managers.

This new edition responds to the developments and advances that have taken place in this area over the last few years, and offers the reader a comprehensive, up-to-date overview of Bayesian statistics

The term probability can be used in two main senses. In the frequency interpretation it is a limiting ratio in a sequence of repeatable events. In the Bayesian view, probability is a mental construct representing uncertainty. This 2002 book is about these two types of probability and investigates how, despite being adopted by scientists and statisticians in the eighteenth and nineteenth centuries, Bayesianism was discredited as a theory of scientific inference during the 1920s and 1930s. Through the examination of a dispute between two British scientists, the author argues that a choice between the two interpretations is not forced by pure logic or the mathematics of the situation, but depends on the experiences and aims of the individuals involved. The book should be of interest to students and scientists interested in statistics and probability theories and to general readers with an interest in the history, sociology and philosophy of science.

This 2002 book investigates the opportunities in building intelligent decision support systems offered by multi-agent distributed probabilistic reasoning. Probabilistic reasoning with graphical models, also known as Bayesian networks or belief networks, has become increasingly an active field of research and practice in artificial intelligence, operations research and statistics. The success of this technique in modeling intelligent decision support systems under the centralized and single-agent paradigm has been striking. Yang Xiang extends graphical dependence models to the distributed and multi-agent paradigm. He identifies the major technical challenges involved in such an endeavor and presents the results. The framework developed in the book allows distributed representation of uncertain knowledge on a large and complex environment embedded in multiple cooperative agents, and effective, exact and distributed probabilistic inference.

A comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, a

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The fi

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The fi

This celebrated primer presents an introduction to all of the key ingredients in understanding computerized adaptive testing technology, test development, statistics, and mental test theory. Based on

Presents an introduction to the concept of data analysis through the use of statistics.

In the new introduction to the award-winning 1999 edition, a Canadian scholar notes that while research on underemployment has increased since then, preoccupation with statistics still emphasizes limi

This is a simple and concise introduction to probability theory. Self-contained and readily accessible, it is written in an informal tutorial style with concepts and techniques defined and developed as necessary. After an elementary discussion of chance, the central and crucial rules and ideas of probability including independence and conditioning are set out. Examples, demonstrations, and exercises are used throughout to explore the ways in which probability is motivated by, and applied to, real life problems in science, medicine, gaming and other subjects of interest. This book is suitable for students taking introductory courses in probability and will provide a solid foundation for more advanced courses in probability and statistics. It would also be a valuable reference to those needing a working knowledge of probability theory and will appeal to anyone interested in this endlessly fascinating and entertaining subject.

On-line learning is one of the most powerful and commonly used techniques for training large layered networks and has been used successfully in many real-world applications. Traditional analytical methods have been recently complemented by ones from statistical physics and Bayesian statistics. This powerful combination of analytical methods provides more insight and deeper understanding of existing algorithms and leads to novel and principled proposals for their improvement. This book presents a coherent picture of the state-of-the-art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall picture. Surveys by leading experts in the field combine new and established material and enable non-experts to learn more about the techniques and methods used. This book, the first in the area, provides a comprehensive view of the subject and will be welcomed by mathematicians, scientists and engineers,

Jeffrey's Theory of probability, first published in 1939, was the first text to develop a fundamental theory of scientific inference based on the ideas of Bayesian statistics. His ideas were way ahead

This book is a short, focused introduction to Mathematica, the comprehensive software system for doing mathematics. Written for the beginning user, this engaging book contains an explanation of essential Mathematica commands, as well as the rich Mathematica interface for preparing polished technical documents. Mathematica can be used to graph functions, solve equations, perform statistics tests, and much more. In addition, it incorporates word processing and desktop publishing features for combining mathematical computations with text and graphics, and producing polished, integrated, interactive documents. You can even use it to create documents and graphics for the Web. This book explains everything you need to know to begin using Mathematica to do all these things and more. Written for Mathematica Version 3, this book can also be used with earlier versions of Mathematica, and even intermediate and advanced users may find useful information here, especially if they are making the swit

This volume is an introduction to stochastic processes and their statistics. Basic stochastic processes are developed from real world situations to the need for generating mathematical models, while a

This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behaviour, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behaviour, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among other applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding

An applied, one-semester introduction to sampling methods for non-mathematics majors that uses simple numerical illustrations to provide an intuitive understanding of concepts and confirm major results. The text describes various methods for sample selection and estimation including unequal probability sampling and the prediction approach. The accompanying disk contains data files for ten cases and two computer programs- one of which is an interactive DOS program designed to serve as a tutorial by assisting the implementation of sampling formulas. The book is intended primarily for upper-level undergraduate or graduate level students of business, government, health administration, economics, political science and other social sciences. It may also be used as a main or supplementary text in service courses on sampling offered by statistics and math departments.

J. Howard Sobel has long been recognized as an important figure in philosophical discussions of rational decision. He has done much to help formulate the concept of causal decision theory. In this volume of essays Sobel explores the Bayesian idea that rational actions maximize expected values, where an action's expected value is a weighted average of its agent's values for its possible total outcomes. Newcomb's Problem and The Prisoner's Dilemma are discussed, and Allais-type puzzles are viewed from the perspective of causal world Bayesianism. The author establishes principles for distinguishing options in decision problems, and studies ways in which perfectly rational causal maximizers can be capable of resolute choices. Sobel also views critically Gauthier's revisionist ideas about maximizing rationality. This collection will be a desideratum for anyone working in the field of rational choice theory, whether in philosophy, economics, political science, psychology or statistics. Howar

Using an informal approach, this is an introduction to a broad range of research methods; presumes no prior experience with statistics and emphasizes theoretical underpinnings and practical applicatio

The study of spatial processes and their applications is an important topic in statistics and finds wide application particularly in computer vision and image processing. This book is devoted to statistical inference in spatial statistics and is intended for specialists needing an introduction to the subject and to its applications. One of the themes of the book is the demonstration of how these techniques give new insights into classical procedures (including new examples in likelihood theory) and newer statistical paradigms such as Monte-Carlo inference and pseudo-likelihood. Professor Ripley also stresses the importance of edge effects and of lack of a unique asymptotic setting in spatial problems. Throughout, the author discusses the foundational issues posed and the difficulties, both computational and philosophical, which arise. The final chapters consider image restoration and segmentation methods and the averaging and summarising of images. Thus, the book will find wide appeal

Reflecting more than 30 years of teaching experience in the field, this guide provides engineers with an introduction to statistics and its applicability to engineering. Examples cover a wide range of

An introduction to the theory and methods of robust statistics, providing students with practical methods for carrying out robust procedures in a variety of statistical contexts and explaining the adv

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric res

Beginners will find this well-respected introduction to statistics and statistical theory a motivating introduction to important mathematical notions such as set, function, and convexity. Other topics

Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries. This book presents some of the algebraic techniques that have been brought to bear on the question of existence, construction and symmetry of symmetric designs – including methods inspired by the algebraic theory of coding and by the representation theory of finite groups – and includes many results. Rich in examples and containing over 100 problems, the text also provides an introduction to many of the modern algebraic approaches used, through six lengthy appendices and supplementary problems. The book will be of interest to both combinatorialists and algebraists, and could be used as a course text for a graduate course.

This is a straightforward and practical introduction to statistics for students without any advanced knowledge of mathematics who need to use statistical techniques. The author provides a wide selection of effective tools of the trade so that the reader can tackle a whole variety of concrete situations. No attempt is made to give a comprehensive account of the subject. Enough technique is explained so that the reader can appreciate when there is a need to turn to more advanced material elsewhere. The basic mathematics required is at the level of senior secondary school education, although even less is necessary for the earlier chapters of the book.

This text is a comprehensive introduction to research methods in social and cultural anthropology. The Peltos focus their discussion on the essential elements of preparing and analyzing the supporting evidence from which generalizations about human nature are derived. The specific elements of anthropological research - such as interviewing informants, observing ceremonial behaviour, and designing surveys - are all covered, but the primary aim is to show how basic observations can be systematically translated into socio-cultural generalizations. The authors place strong emphasis not only on quantification and statistics, but also on the more qualitative aspects of anthropological working styles that are essential to effective research. The two main themes of the book can be stated as follows: (1) anthropological generalizations and more complex theoretical structures can be built up only through careful implementation of basic concepts, the building blocks of all theory, and (2) success

Designed for readers with a background in basic algebra, this best-selling introduction to statistics for business and economics emphasizes inference?with extensive coverage of data collection and ana

This is a lucid introduction to some of the mathematical ideas which are useful to biologists. Professor Maynard Smith introduces the reader to the ways in which biological problems can be expressed mathematically, and shows how the mathematical equations which arise in biological work can be solved. Each chapter has a number of examples which present further points of biological and mathematical interest. interest. Professor Maynard Smith's book is written for all biologists, from undergraduate level upwards, who need mathematical tools. Only an elementary knowledge of mathematics is assumed. Since there are already a number of books dealing with statistics for biologists, this book is particularly concerned with non-statistical topics.

Now in its fourth edition, Behavioral Research and Analysis: An Introduction to Statistics within the Context of Experimental Design presents an overview of statistical methods within the context of e

This book provides a short and concise introduction to Bayesian optimization specifically for experimental and computational materials scientists. After explaining the basic idea behind Bayesian optim

Designed for a two-semester, introductory course for graduate students in the social sciences, this text illustrates how to use R to apply both standard and modern methods to correct known problems wi

This book provides an essential guide to the mathematical concepts, techniques, and calculations a student in the pharmaceutical sciences is likely to encounter.

This book provides an essential guide to the mathematical concepts, techniques, and calculations a student in the pharmaceutical sciences is likely to encounter. Using a wide range of worked examples,

The subject of data-driven modeling has been addressed in various disciplines such as statistics, pattern recognition, signal processing, genomics, artificial neural networks, machine learning, and d

This introduction to social statistics, with clear, well-illustrated instructions for using SPSS software, emphasizes the interpretation of statistics and applications to real-world situations.