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The Probabilistic Method

Author : Noga Alon
Publisher : John Wiley & Sons
ISBN 13 : 1119062071
Total Pages : 396 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis The Probabilistic Method by : Noga Alon

Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.

Probabilistic Methods for Algorithmic Discrete Mathematics

Author : Michel Habib
Publisher : Springer Science & Business Media
ISBN 13 : 3662127881
Total Pages : 342 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Probabilistic Methods for Algorithmic Discrete Mathematics by : Michel Habib

Download or read book Probabilistic Methods for Algorithmic Discrete Mathematics written by Michel Habib and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

Probabilistic Techniques in Analysis

Author : Richard F. Bass
Publisher : Springer Science & Business Media
ISBN 13 : 0387943870
Total Pages : 408 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Probabilistic Techniques in Analysis by : Richard F. Bass

Download or read book Probabilistic Techniques in Analysis written by Richard F. Bass and published by Springer Science & Business Media. This book was released on 1994-12-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Graph Colouring and the Probabilistic Method

Author : Michael Molloy
Publisher : Springer Science & Business Media
ISBN 13 : 3642040160
Total Pages : 320 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Graph Colouring and the Probabilistic Method by : Michael Molloy

Download or read book Graph Colouring and the Probabilistic Method written by Michael Molloy and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past decade, many major advances have been made in the field of graph coloring via the probabilistic method. This monograph, by two of the best on the topic, provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.

Ten Lectures on the Probabilistic Method

Author : Joel Spencer
Publisher : SIAM
ISBN 13 : 9781611970074
Total Pages : 98 pages
Book Rating : 4.9/5 (7 download)

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Book Synopsis Ten Lectures on the Probabilistic Method by : Joel Spencer

Download or read book Ten Lectures on the Probabilistic Method written by Joel Spencer and published by SIAM. This book was released on 1994-01-01 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. The book is not encyclopedic--it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colorings) by showing that an appropriately defined random object has positive probability of having those properties.

Probabilistic Methods for Bioinformatics

Author : Richard E. Neapolitan
Publisher : Morgan Kaufmann
ISBN 13 : 0080919367
Total Pages : 421 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Probabilistic Methods for Bioinformatics by : Richard E. Neapolitan

Download or read book Probabilistic Methods for Bioinformatics written by Richard E. Neapolitan and published by Morgan Kaufmann. This book was released on 2009-06-12 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bayesian network is one of the most important architectures for representing and reasoning with multivariate probability distributions. When used in conjunction with specialized informatics, possibilities of real-world applications are achieved. Probabilistic Methods for BioInformatics explains the application of probability and statistics, in particular Bayesian networks, to genetics. This book provides background material on probability, statistics, and genetics, and then moves on to discuss Bayesian networks and applications to bioinformatics. Rather than getting bogged down in proofs and algorithms, probabilistic methods used for biological information and Bayesian networks are explained in an accessible way using applications and case studies. The many useful applications of Bayesian networks that have been developed in the past 10 years are discussed. Forming a review of all the significant work in the field that will arguably become the most prevalent method in biological data analysis. - Unique coverage of probabilistic reasoning methods applied to bioinformatics data--those methods that are likely to become the standard analysis tools for bioinformatics. - Shares insights about when and why probabilistic methods can and cannot be used effectively; - Complete review of Bayesian networks and probabilistic methods with a practical approach.

Probability and Computing

Author : Michael Mitzenmacher
Publisher : Cambridge University Press
ISBN 13 : 9780521835404
Total Pages : 372 pages
Book Rating : 4.8/5 (354 download)

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Book Synopsis Probability and Computing by : Michael Mitzenmacher

Download or read book Probability and Computing written by Michael Mitzenmacher and published by Cambridge University Press. This book was released on 2005-01-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.

Bayesian Methods for Hackers

Author : Cameron Davidson-Pilon
Publisher : Addison-Wesley Professional
ISBN 13 : 0133902927
Total Pages : 551 pages
Book Rating : 4.1/5 (339 download)

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Book Synopsis Bayesian Methods for Hackers by : Cameron Davidson-Pilon

Download or read book Bayesian Methods for Hackers written by Cameron Davidson-Pilon and published by Addison-Wesley Professional. This book was released on 2015-09-30 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master Bayesian Inference through Practical Examples and Computation–Without Advanced Mathematical Analysis Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You’ll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you’ve mastered these techniques, you’ll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes • Learning the Bayesian “state of mind” and its practical implications • Understanding how computers perform Bayesian inference • Using the PyMC Python library to program Bayesian analyses • Building and debugging models with PyMC • Testing your model’s “goodness of fit” • Opening the “black box” of the Markov Chain Monte Carlo algorithm to see how and why it works • Leveraging the power of the “Law of Large Numbers” • Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning • Using loss functions to measure an estimate’s weaknesses based on your goals and desired outcomes • Selecting appropriate priors and understanding how their influence changes with dataset size • Overcoming the “exploration versus exploitation” dilemma: deciding when “pretty good” is good enough • Using Bayesian inference to improve A/B testing • Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.

Probabilistic Risk Analysis

Author : Tim Bedford
Publisher : Cambridge University Press
ISBN 13 : 9780521773201
Total Pages : 228 pages
Book Rating : 4.7/5 (732 download)

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Book Synopsis Probabilistic Risk Analysis by : Tim Bedford

Download or read book Probabilistic Risk Analysis written by Tim Bedford and published by Cambridge University Press. This book was released on 2001-04-30 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic risk analysis aims to quantify the risk caused by high technology installations. Increasingly, such analyses are being applied to a wider class of systems in which problems such as lack of data, complexity of the systems, uncertainty about consequences, make a classical statistical analysis difficult or impossible. The authors discuss the fundamental notion of uncertainty, its relationship with probability, and the limits to the quantification of uncertainty. Drawing on extensive experience in the theory and applications of risk analysis, the authors focus on the conceptual and mathematical foundations underlying the quantification, interpretation and management of risk. They cover standard topics as well as important new subjects such as the use of expert judgement and uncertainty propagation. The relationship of risk analysis with decision making is highlighted in chapters on influence diagrams and decision theory. Finally, the difficulties of choosing metrics to quantify risk, and current regulatory frameworks are discussed.

Probabilistic Machine Learning

Author : Kevin P. Murphy
Publisher : MIT Press
ISBN 13 : 0262369303
Total Pages : 858 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Probabilistic Machine Learning by : Kevin P. Murphy

Download or read book Probabilistic Machine Learning written by Kevin P. Murphy and published by MIT Press. This book was released on 2022-03-01 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 new book is accompanied by online Python code, using libraries such as scikit-learn, JAX, PyTorch, and Tensorflow, which can be used to reproduce nearly all the figures; this code can be run inside a web browser using cloud-based notebooks, and provides a practical complement to the theoretical topics discussed in the book. This introductory text will be followed by a sequel that covers more advanced topics, taking the same probabilistic approach.

Probabilistic Methods of Signal and System Analysis

Author : George R. Cooper
Publisher : Oxford Series in Electrical an
ISBN 13 : 9780195123548
Total Pages : 480 pages
Book Rating : 4.1/5 (235 download)

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Book Synopsis Probabilistic Methods of Signal and System Analysis by : George R. Cooper

Download or read book Probabilistic Methods of Signal and System Analysis written by George R. Cooper and published by Oxford Series in Electrical an. This book was released on 1999 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Methods of Signal and System Analysis, 3/e stresses the engineering applications of probability theory, presenting the material at a level and in a manner ideally suited to engineering students at the junior or senior level. It is also useful as a review for graduate students and practicing engineers. Thoroughly revised and updated, this third edition incorporates increased use of the computer in both text examples and selected problems. It utilizes MATLAB as a computational tool and includes new sections relating to Bernoulli trials, correlation of data sets, smoothing of data, computer computation of correlation functions and spectral densities, and computer simulation of systems. All computer examples can be run using the Student Version of MATLAB. Almost all of the examples and many of the problems have been modified or changed entirely, and a number of new problems have been added. A separate appendix discusses and illustrates the application of computers to signal and system analysis.

Probability and Algorithms

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309047765
Total Pages : 189 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis Probability and Algorithms by : National Research Council

Download or read book Probability and Algorithms written by National Research Council and published by National Academies Press. This book was released on 1992-02-01 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the hardest computational problems have been successfully attacked through the use of probabilistic algorithms, which have an element of randomness to them. Concepts from the field of probability are also increasingly useful in analyzing the performance of algorithms, broadening our understanding beyond that provided by the worst-case or average-case analyses. This book surveys both of these emerging areas on the interface of the mathematical sciences and computer science. It is designed to attract new researchers to this area and provide them with enough background to begin explorations of their own.

A Probabilistic Theory of Pattern Recognition

Author : Luc Devroye
Publisher : Springer Science & Business Media
ISBN 13 : 1461207118
Total Pages : 631 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis A Probabilistic Theory of Pattern Recognition by : Luc Devroye

Download or read book A Probabilistic Theory of Pattern Recognition written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modern Probabilistic Methods for Analysis of Telecommunication Networks

Author : Alexander Dudin
Publisher : Springer
ISBN 13 : 3642359809
Total Pages : 224 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Modern Probabilistic Methods for Analysis of Telecommunication Networks by : Alexander Dudin

Download or read book Modern Probabilistic Methods for Analysis of Telecommunication Networks written by Alexander Dudin and published by Springer. This book was released on 2012-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Conference on Modern Probabilistic Methods for Analysis of Telecommunication Networks, Belarusian Winter Workshop in Queueing Theory, BWWQT 2013, held in Minsk, Belarus, in January 2013. The 23 revised full papers presented were carefully reviewed and selected from numerous submissions. The papers present new results in study and optimization of information transmission models in telecommunication networks using different approaches, mainly based on theories of queueing systems and queueing networks.

Machine Learning

Author : Kevin P. Murphy
Publisher : MIT Press
ISBN 13 : 0262018020
Total Pages : 1102 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Machine Learning by : Kevin P. Murphy

Download or read book Machine Learning written by Kevin P. Murphy and published by MIT Press. This book was released on 2012-08-24 with total page 1102 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach. Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package—PMTK (probabilistic modeling toolkit)—that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Probabilistic Robotics

Author : Sebastian Thrun
Publisher : MIT Press
ISBN 13 : 0262201623
Total Pages : 668 pages
Book Rating : 4.2/5 (622 download)

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Book Synopsis Probabilistic Robotics by : Sebastian Thrun

Download or read book Probabilistic Robotics written by Sebastian Thrun and published by MIT Press. This book was released on 2005-08-19 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the techniques and algorithms of the newest field in robotics. Probabilistic robotics is a new and growing area in robotics, concerned with perception and control in the face of uncertainty. Building on the field of mathematical statistics, probabilistic robotics endows robots with a new level of robustness in real-world situations. This book introduces the reader to a wealth of techniques and algorithms in the field. All algorithms are based on a single overarching mathematical foundation. Each chapter provides example implementations in pseudo code, detailed mathematical derivations, discussions from a practitioner's perspective, and extensive lists of exercises and class projects. The book's Web site, www.probabilistic-robotics.org, has additional material. The book is relevant for anyone involved in robotic software development and scientific research. It will also be of interest to applied statisticians and engineers dealing with real-world sensor data.