Bayesian nets are widely used in artificial intelligence as a calculus for causal reasoning, enabling machines to make predictions, perform diagnoses, take decisions and even to discover causal relationships. But many philosophers have criticised and ultimately rejected the central assumption on which such work is based - the Causal Markov Condition. So should Bayesian nets be abandoned? What explains their success in artificial intelligence? This book argues that the Causal Markov Condition holds as a default rule: it often holds but may need to be repealed in the face of counterexamples. Thus Bayesian nets are the right tool to use by default but naively applying them can lead to problems. The book develops a systematic account of causal reasoning and shows how Bayesian nets can be coherently employed to automate the reasoning processes of an artificial agent. The resulting framework for causal reasoning involves not only new algorithms but also new conceptual foundations. Probability and causality are treated as mental notions - part of an agent's belief state.Yet probability and causality are also objective - different agents with the same background knowledge ought to adopt the same or similar probabilistic and causal beliefs. This book, aimed at researchers and graduate students in computer science, mathematics and philosophy, provides a general introduction to these philosophical views as well as an exposition of the computational techniques that they motivate.

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.
Clarifies both traditional methods and current, popular algorithms (e.g. neural nets, random forests)
Written by two world-leading researchers
Addressed to all fields that work with data

A self-contained and coherent account of probabilistic techniques, covering: distance measures, kernel rules, nearest neighbour rules, Vapnik-Chervonenkis theory, parametric classification, and feature extraction. Each chapter concludes with problems and exercises to further the readers understanding. Both research workers and graduate students will benefit from this wide-ranging and up-to-date account of a fast- moving field.

This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author's lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Cinlar has received many awards for excellence in teaching, including the President's Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.

Probability and Measure Anniversary Edition This Anniversary Edition of Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining intact the unique approach of the Third Edition , this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory, which is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, stochastic processes, Brownian motion, and ergodic theory. The Anniversary Edition features a new, pedagogically sound interior design with an emphasis on open space.Like the previous editions, this Anniversary Edition will be well received by students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.

The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data. Calculus is assumed as a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.

Publisher : Springer; 1997th edition (October 17, 1997)
Language : English
Hardcover : 279 pages
ISBN-10 : 0387982272
ISBN-13 : 978-0387982274
Item Weight : 2.8 pounds
Dimensions : 6.14 x 0.69 x 9.21 inches
Intended as a first course in probability at post-calculus level, this book is of special interest to students majoring in computer science as well as in mathematics. Since calculus is used only occasionally in the text, students who have forgotten their calculus can nevertheless easily understand the book, and its slow, gentle style and clear exposition will also appeal. Basic concepts such as counting, independence, conditional probability, random variables, approximation of probabilities, generating functions, random walks and Markov chains are all clearly explained and backed by many worked exercises. The 1,196 numerical answers to the 405 exercises, many with multiple parts, are included at the end of the book, and throughout, there are various historical comments on the study of probability. These include biographical information on such famous contributors as Fermat, Pascal, the Bernoullis, DeMoivre, Bayes, Laplace, Poisson, and Markov. Of interest to a wide range of readers and useful in many undergraduate programs.

This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The new edition begins with a short chapter on measure theory to orient readers new to the subject.

Highly useful text studies the logarithmic measures of information and their application to testing statistical hypotheses. Topics include introduction and definition of measures of information, their relationship to Fisher's information measure and sufficiency, fundamental inequalities of information theory, much more. Numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.

A systematic account of the theory of probability for certain sample spaces with algebraic structure, this text covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results rather than on general and complete answers. 1963 edition.

The past decade has seen a dramatic increase in the use of Bayesian methods in marketing due, in part, to computational and modelling breakthroughs, making its implementation ideal for many marketing problems. Bayesian analyses can now be conducted over a wide range of marketing problems, from new product introduction to pricing, and with a wide variety of different data sources.
Bayesian Statistics and Marketing describes the basic advantages of the Bayesian approach, detailing the nature of the computational revolution. Examples contained include household and consumer panel data on product purchases and survey data, demand models based on micro-economic theory and random effect models used to pool data among respondents. The book also discusses the theory and practical use of MCMC methods.
Written by the leading experts in the field, this unique book:

Presents a unified treatment of Bayesian methods in marketing, with common notation and algorithms for estimating the models.
Provides a self-contained introduction to Bayesian methods.
Includes case studies drawn from the authors’ recent research to illustrate how Bayesian methods can be extended to apply to many important marketing problems.
Is accompanied by an R package, bayesm, which implements all of the models and methods in the book and includes many datasets. In addition the book’s website hosts datasets and R code for the case studies. Bayesian Statistics and Marketing provides a platform for researchers in marketing to analyse their data with state-of-the-art methods and develop new models of consumer behaviour. It provides a unified reference for cutting-edge marketing researchers, as well as an invaluable guide to this growing area for both graduate students and professors, alike.

The methodology used to construct tree structured rules is the focus of this monograph. Unlike many other statistical procedures, which moved from pencil and paper to calculators, this text's use of trees was unthinkable before computers. Both the practical and theoretical sides have been developed in the authors' study of tree methods. Classification and Regression Trees reflects these two sides, covering the use of trees as a data analysis method, and in a more mathematical framework, proving some of their fundamental properties.

Builds on classical probability theory and offers an extremely workable solution to the many problems of artificial intelligence, concentrating on the rapidly growing areas of fuzzy reasoning and neural computing. Contains a collection of previously unpublished articles by leading researchers in the field.