Bayes' Rule

A Tutorial Introduction to Bayesian Analysis

Author: James V. Stone

Publisher: Sebtel Press

ISBN: 0956372848

Category: Bayesian statistical decision theory

Page: 170

View: 4629

In this richly illustrated book, a range of accessible examples are used to show how Bayes' rule is actually a natural consequence of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for the novice who wishes to become familiar with the basic principles of Bayesian analysis.
Posted in Bayesian statistical decision theory

Bayes' Rule with MatLab

A Tutorial Introduction to Bayesian Analysis

Author: James V Stone

Publisher: N.A

ISBN: 9780993367908

Category: Mathematics

Page: 192

View: 4398

Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, a range of accessible examples is used to show how Bayes' rule is actually a natural consequence of common sense reasoning. Bayes' rule is then derived using intuitive graphical representations of probability, and Bayesian analysis is applied to parameter estimation using the MatLab and Python programs provided online. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to become familiar with the basic principles of Bayesian analysis. Note that this MatLab version of Bayes' Rule includes working MatLab code snippets alongside the relevant equations.
Posted in Mathematics

Independent Component Analysis

A Tutorial Introduction

Author: James V. Stone

Publisher: MIT Press

ISBN: 9780262693158

Category: Mathematics

Page: 193

View: 6187

A tutorial-style introduction to a class of methods for extracting independent signals from a mixture of signals originating from different physical sources; includes MatLab computer code examples.
Posted in Mathematics

Information Theory

A Tutorial Introduction

Author: JV Stone

Publisher: Sebtel Press

ISBN: 0956372856

Category: Information theory

Page: 243

View: 4866

Originally developed by Claude Shannon in the 1940s, information theory laid the foundations for the digital revolution, and is now an essential tool in telecommunications, genetics, linguistics, brain sciences, and deep space communication. In this richly illustrated book, accessible examples are used to introduce information theory in terms of everyday games like ‘20 questions’ before more advanced topics are explored. Online MatLab and Python computer programs provide hands-on experience of information theory in action, and PowerPoint slides give support for teaching. Written in an informal style, with a comprehensive glossary and tutorial appendices, this text is an ideal primer for novices who wish to learn the essential principles and applications of information theory.
Posted in Information theory

Bayesian Reasoning and Machine Learning

Author: David Barber

Publisher: Cambridge University Press

ISBN: 0521518148

Category: Computers

Page: 697

View: 9039

A practical introduction perfect for final-year undergraduate and graduate students without a solid background in linear algebra and calculus.
Posted in Computers

Bayesian Signal Processing

Classical, Modern, and Particle Filtering Methods

Author: James V. Candy

Publisher: John Wiley & Sons

ISBN: 1119125456

Category: Technology & Engineering

Page: 640

View: 8726

Presents the Bayesian approach to statistical signal processing for a variety of useful model sets This book aims to give readers a unified Bayesian treatment starting from the basics (Bayes’ rule) to the more advanced (Monte Carlo sampling), evolving to the next-generation model-based techniques (sequential Monte Carlo sampling). This next edition incorporates a new chapter on “Sequential Bayesian Detection,” a new section on “Ensemble Kalman Filters” as well as an expansion of Case Studies that detail Bayesian solutions for a variety of applications. These studies illustrate Bayesian approaches to real-world problems incorporating detailed particle filter designs, adaptive particle filters and sequential Bayesian detectors. In addition to these major developments a variety of sections are expanded to ``fill-in-the gaps" of the first edition. Here metrics for particle filter (PF) designs with emphasis on classical ``sanity testing" lead to ensemble techniques as a basic requirement for performance analysis. The expansion of information theoretic metrics and their application to PF designs is fully developed and applied. These expansions of the book have been updated to provide a more cohesive discussion of Bayesian processing with examples and applications enabling the comprehension of alternative approaches to solving estimation/detection problems. The second edition of Bayesian Signal Processing features: “Classical” Kalman filtering for linear, linearized, and nonlinear systems; “modern” unscented and ensemble Kalman filters; and the “next-generation” Bayesian particle filters Sequential Bayesian detection techniques incorporating model-based schemes for a variety of real-world problems Practical Bayesian processor designs including comprehensive methods of performance analysis ranging from simple sanity testing and ensemble techniques to sophisticated information metrics New case studies on adaptive particle filtering and sequential Bayesian detection are covered detailing more Bayesian approaches to applied problem solving MATLAB® notes at the end of each chapter help readers solve complex problems using readily available software commands and point out other software packages available Problem sets to test readers’ knowledge and help them put their new skills into practice Bayesian Signal Processing, Second Edition is written for all students, scientists, and engineers who investigate and apply signal processing to their everyday problems. JAMES V. CANDY, PhD, is Chief Scientist for Engineering, a Distinguished Member of the Technical Staff, founder, and former director of the Center for Advanced Signal & Image Sciences at the Lawrence Livermore National Laboratory. He is also an Adjunct Full Professor at the University of California, Santa Barbara, a Fellow of the IEEE, and a Fellow of the Acoustical Society of America. Dr. Candy has published more than 225 journal articles, book chapters, and technical reports. He is also the author of Signal Processing: Model-Based Approach, Signal Processing: A Modern Approach, and Model-Based Signal Processing (Wiley 2006). Dr. Candy was awarded the IEEE Distinguished Technical Achievement Award for his development of model-based signal processing and the Acoustical Society of America Helmholtz-Rayleigh Interdisciplinary Silver Medal for his contributions to acoustical signal processing and underwater acoustics.
Posted in Technology & Engineering

Statistics for Bioengineering Sciences

With MATLAB and WinBUGS Support

Author: Brani Vidakovic

Publisher: Springer Science & Business Media

ISBN: 9781461403944

Category: Mathematics

Page: 753

View: 4198

Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing engineering fields, bioengineering and biomedical engineering, while implementing software that engineers are familiar with. The author integrates introductory statistics for engineers and introductory biostatistics as a single textbook heavily oriented to computation and hands on approaches. For example, topics ranging from the aspects of disease and device testing, Sensitivity, Specificity and ROC curves, Epidemiological Risk Theory, Survival Analysis, or Logistic and Poisson Regressions are covered. In addition to the synergy of engineering and biostatistical approaches, the novelty of this book is in the substantial coverage of Bayesian approaches to statistical inference. Many examples in this text are solved using both the traditional and Bayesian methods, and the results are compared and commented.
Posted in Mathematics

Engineering Biostatistics

An Introduction Using MATLAB and WinBUGS

Author: Brani Vidakovic

Publisher: John Wiley & Sons

ISBN: 1119168961

Category: Mathematics

Page: 984

View: 5282

Provides a one-stop resource for engineers learning biostatistics using MATLAB® and WinBUGS Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing bio-oriented engineering fields while implementing software packages that are familiar to engineers. The book is heavily oriented to computation and hands-on approaches so readers understand each step of the programming. Another dimension of this book is in parallel coverage of both Bayesian and frequentist approaches to statistical inference. It avoids taking sides on the classical vs. Bayesian paradigms, and many examples in this book are solved using both methods. The results are then compared and commented upon. Readers have the choice of MATLAB® for classical data analysis and WinBUGS/OpenBUGS for Bayesian data analysis. Every chapter starts with a box highlighting what is covered in that chapter and ends with exercises, a list of software scripts, datasets, and references. Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS also includes: parallel coverage of classical and Bayesian approaches, where appropriate substantial coverage of Bayesian approaches to statistical inference material that has been classroom-tested in an introductory statistics course in bioengineering over several years exercises at the end of each chapter and an accompanying website with full solutions and hints to some exercises, as well as additional materials and examples Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS can serve as a textbook for introductory-to-intermediate applied statistics courses, as well as a useful reference for engineers interested in biostatistical approaches.
Posted in Mathematics

Fundamentals of Digital Image Processing

A Practical Approach with Examples in Matlab

Author: Chris Solomon,Toby Breckon

Publisher: John Wiley & Sons

ISBN: 1119957001

Category: Science

Page: 344

View: 690

This is an introductory to intermediate level text on the science of image processing, which employs the Matlab programming language to illustrate some of the elementary, key concepts in modern image processing and pattern recognition. The approach taken is essentially practical and the book offers a framework within which the concepts can be understood by a series of well chosen examples, exercises and computer experiments, drawing on specific examples from within science, medicine and engineering. Clearly divided into eleven distinct chapters, the book begins with a fast-start introduction to image processing to enhance the accessibility of later topics. Subsequent chapters offer increasingly advanced discussion of topics involving more challenging concepts, with the final chapter looking at the application of automated image classification (with Matlab examples) . Matlab is frequently used in the book as a tool for demonstrations, conducting experiments and for solving problems, as it is both ideally suited to this role and is widely available. Prior experience of Matlab is not required and those without access to Matlab can still benefit from the independent presentation of topics and numerous examples. Features a companion website www.wiley.com/go/solomon/fundamentals containing a Matlab fast-start primer, further exercises, examples, instructor resources and accessibility to all files corresponding to the examples and exercises within the book itself. Includes numerous examples, graded exercises and computer experiments to support both students and instructors alike.
Posted in Science

Computational Statistics Handbook with MATLAB, Third Edition

Author: Wendy L. Martinez,Angel R. Martinez

Publisher: CRC Press

ISBN: 1466592745

Category: Business & Economics

Page: 731

View: 9688

A Strong Practical Focus on Applications and Algorithms Computational Statistics Handbook with MATLAB®, Third Edition covers today’s most commonly used techniques in computational statistics while maintaining the same philosophy and writing style of the bestselling previous editions. The text keeps theoretical concepts to a minimum, emphasizing the implementation of the methods. New to the Third Edition This third edition is updated with the latest version of MATLAB and the corresponding version of the Statistics and Machine Learning Toolbox. It also incorporates new sections on the nearest neighbor classifier, support vector machines, model checking and regularization, partial least squares regression, and multivariate adaptive regression splines. Web Resource The authors include algorithmic descriptions of the procedures as well as examples that illustrate the use of algorithms in data analysis. The MATLAB code, examples, and data sets are available online.
Posted in Business & Economics

Intuitive Probability and Random Processes using MATLAB®

Author: Steven Kay

Publisher: Springer Science & Business Media

ISBN: 0387241582

Category: Technology & Engineering

Page: 834

View: 4728

Intuitive Probability and Random Processes using MATLAB® is an introduction to probability and random processes that merges theory with practice. Based on the author’s belief that only "hands-on" experience with the material can promote intuitive understanding, the approach is to motivate the need for theory using MATLAB examples, followed by theory and analysis, and finally descriptions of "real-world" examples to acquaint the reader with a wide variety of applications. The latter is intended to answer the usual question "Why do we have to study this?" Other salient features are: *heavy reliance on computer simulation for illustration and student exercises *the incorporation of MATLAB programs and code segments *discussion of discrete random variables followed by continuous random variables to minimize confusion *summary sections at the beginning of each chapter *in-line equation explanations *warnings on common errors and pitfalls *over 750 problems designed to help the reader assimilate and extend the concepts Intuitive Probability and Random Processes using MATLAB® is intended for undergraduate and first-year graduate students in engineering. The practicing engineer as well as others having the appropriate mathematical background will also benefit from this book. About the Author Steven M. Kay is a Professor of Electrical Engineering at the University of Rhode Island and a leading expert in signal processing. He has received the Education Award "for outstanding contributions in education and in writing scholarly books and texts..." from the IEEE Signal Processing society and has been listed as among the 250 most cited researchers in the world in engineering.
Posted in Technology & Engineering

MATLAB for Neuroscientists

An Introduction to Scientific Computing in MATLAB

Author: Pascal Wallisch,Michael E. Lusignan,Marc D. Benayoun,Tanya I. Baker,Adam Seth Dickey,Nicholas G. Hatsopoulos

Publisher: Academic Press

ISBN: 0123838371

Category: Computers

Page: 570

View: 3202

MATLAB for Neuroscientists serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that a wide variety of computational problems can be addressed in a single programming environment. This updated edition features additional material on the creation of visual stimuli, advanced psychophysics, analysis of LFP data, choice probabilities, synchrony, and advanced spectral analysis. Users at a variety of levels—advanced undergraduates, beginning graduate students, and researchers looking to modernize their skills—will learn to design and implement their own analytical tools, and gain the fluency required to meet the computational needs of neuroscience practitioners. The first complete volume on MATLAB focusing on neuroscience and psychology applications Problem-based approach with many examples from neuroscience and cognitive psychology using real data Illustrated in full color throughout Careful tutorial approach, by authors who are award-winning educators with strong teaching experience
Posted in Computers

Bayesian Filtering and Smoothing

Author: Simo Särkkä

Publisher: Cambridge University Press

ISBN: 110703065X

Category: Computers

Page: 254

View: 7609

A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Posted in Computers

Exploratory Data Analysis with MATLAB, Third Edition

Author: Wendy L. Martinez,Angel R. Martinez,Jeffrey Solka

Publisher: CRC Press

ISBN: 1315349841

Category: Mathematics

Page: 590

View: 7415

Praise for the Second Edition: "The authors present an intuitive and easy-to-read book. ... accompanied by many examples, proposed exercises, good references, and comprehensive appendices that initiate the reader unfamiliar with MATLAB." —Adolfo Alvarez Pinto, International Statistical Review "Practitioners of EDA who use MATLAB will want a copy of this book. ... The authors have done a great service by bringing together so many EDA routines, but their main accomplishment in this dynamic text is providing the understanding and tools to do EDA. —David A Huckaby, MAA Reviews Exploratory Data Analysis (EDA) is an important part of the data analysis process. The methods presented in this text are ones that should be in the toolkit of every data scientist. As computational sophistication has increased and data sets have grown in size and complexity, EDA has become an even more important process for visualizing and summarizing data before making assumptions to generate hypotheses and models. Exploratory Data Analysis with MATLAB, Third Edition presents EDA methods from a computational perspective and uses numerous examples and applications to show how the methods are used in practice. The authors use MATLAB code, pseudo-code, and algorithm descriptions to illustrate the concepts. The MATLAB code for examples, data sets, and the EDA Toolbox are available for download on the book’s website. New to the Third Edition Random projections and estimating local intrinsic dimensionality Deep learning autoencoders and stochastic neighbor embedding Minimum spanning tree and additional cluster validity indices Kernel density estimation Plots for visualizing data distributions, such as beanplots and violin plots A chapter on visualizing categorical data
Posted in Mathematics

Vision and Brain

How We Perceive the World

Author: Dr James V Stone

Publisher: MIT Press

ISBN: 0262517736

Category: Health & Fitness

Page: 243

View: 7283

In this accessible and engaging introduction to modern vision science, James Stone uses visual illusions to explore how the brain sees the world. Understanding vision, Stone argues, is not simply a question of knowing which neurons respond to particular visual features, but also requires a computational theory of vision. Stone draws together results from David Marr's computational framework, Barlow's efficient coding hypothesis, Bayesian inference, Shannon's information theory, and signal processing to construct a coherent account of vision that explains not only how the brain is fooled by particular visual illusions, but also why any biological or computer vision system should also be fooled by these illusions. This short text includes chapters on the eye and its evolution, how and why visual neurons from different species encode the retinal image in the same way, how information theory explains color aftereffects, how different visual cues provide depth information, how the imperfect visual information received by the eye and brain can be rescued by Bayesian inference, how different brain regions process visual information, and the bizarre perceptual consequences that result from damage to these brain regions. The tutorial style emphasizes key conceptual insights, rather than mathematical details, making the book accessible to the nonscientist and suitable for undergraduate or postgraduate study.
Posted in Health & Fitness

Bayesian Cognitive Modeling

A Practical Course

Author: Michael D. Lee,Eric-Jan Wagenmakers

Publisher: Cambridge University Press

ISBN: 1107018455

Category: Computers

Page: 280

View: 5751

Using a practical, hands-on approach, this book will teach anyone how to carry out Bayesian analyses and interpret the results.
Posted in Computers

Random Signals and Processes Primer with MATLAB

Author: Gordana Jovanovic Dolecek

Publisher: Springer Science & Business Media

ISBN: 1461423864

Category: Technology & Engineering

Page: 530

View: 5319

This book provides anyone needing a primer on random signals and processes with a highly accessible introduction to these topics. It assumes a minimal amount of mathematical background and focuses on concepts, related terms and interesting applications to a variety of fields. All of this is motivated by numerous examples implemented with MATLAB, as well as a variety of exercises at the end of each chapter.
Posted in Technology & Engineering

Computational Statistics Handbook with MATLAB, Third Edition

Author: Wendy L. Martinez,Angel R. Martinez

Publisher: CRC Press

ISBN: 1466592745

Category: Business & Economics

Page: 731

View: 875

A Strong Practical Focus on Applications and Algorithms Computational Statistics Handbook with MATLAB®, Third Edition covers today’s most commonly used techniques in computational statistics while maintaining the same philosophy and writing style of the bestselling previous editions. The text keeps theoretical concepts to a minimum, emphasizing the implementation of the methods. New to the Third Edition This third edition is updated with the latest version of MATLAB and the corresponding version of the Statistics and Machine Learning Toolbox. It also incorporates new sections on the nearest neighbor classifier, support vector machines, model checking and regularization, partial least squares regression, and multivariate adaptive regression splines. Web Resource The authors include algorithmic descriptions of the procedures as well as examples that illustrate the use of algorithms in data analysis. The MATLAB code, examples, and data sets are available online.
Posted in Business & Economics

Machine Learning

A Bayesian and Optimization Perspective

Author: Sergios Theodoridis

Publisher: Academic Press

ISBN: 0128017228

Category: Computers

Page: 1062

View: 3213

This tutorial text gives a unifying perspective on machine learning by covering both probabilistic and deterministic approaches -which are based on optimization techniques – together with the Bayesian inference approach, whose essence lies in the use of a hierarchy of probabilistic models. The book presents the major machine learning methods as they have been developed in different disciplines, such as statistics, statistical and adaptive signal processing and computer science. Focusing on the physical reasoning behind the mathematics, all the various methods and techniques are explained in depth, supported by examples and problems, giving an invaluable resource to the student and researcher for understanding and applying machine learning concepts. The book builds carefully from the basic classical methods to the most recent trends, with chapters written to be as self-contained as possible, making the text suitable for different courses: pattern recognition, statistical/adaptive signal processing, statistical/Bayesian learning, as well as short courses on sparse modeling, deep learning, and probabilistic graphical models. All major classical techniques: Mean/Least-Squares regression and filtering, Kalman filtering, stochastic approximation and online learning, Bayesian classification, decision trees, logistic regression and boosting methods. The latest trends: Sparsity, convex analysis and optimization, online distributed algorithms, learning in RKH spaces, Bayesian inference, graphical and hidden Markov models, particle filtering, deep learning, dictionary learning and latent variables modeling. Case studies - protein folding prediction, optical character recognition, text authorship identification, fMRI data analysis, change point detection, hyperspectral image unmixing, target localization, channel equalization and echo cancellation, show how the theory can be applied. MATLAB code for all the main algorithms are available on an accompanying website, enabling the reader to experiment with the code.
Posted in Computers

NETLAB

Algorithms for Pattern Recognition

Author: Ian Nabney

Publisher: Springer Science & Business Media

ISBN: 9781852334406

Category: Computers

Page: 420

View: 814

This volume provides students, researchers and application developers with the knowledge and tools to get the most out of using neural networks and related data modelling techniques to solve pattern recognition problems. Each chapter covers a group of related pattern recognition techniques and includes a range of examples to show how these techniques can be applied to solve practical problems. Features of particular interest include: - A NETLAB toolbox which is freely available - Worked examples, demonstration programs and over 100 graded exercises - Cutting edge research made accessible for the first time in a highly usable form - Comprehensive coverage of visualisation methods, Bayesian techniques for neural networks and Gaussian Processes Although primarily a textbook for teaching undergraduate and postgraduate courses in pattern recognition and neural networks, this book will also be of interest to practitioners and researchers who can use the toolbox to develop application solutions and new models. "...provides a unique collection of many of the most important pattern recognition algorithms. With its use of compact and easily modified MATLAB scripts, the book is ideally suited to both teaching and research." Christopher Bishop, Microsoft Research, Cambridge, UK "...a welcome addition to the literature on neural networks and how to train and use them to solve many of the statistical problems that occur in data analysis and data mining" Jack Cowan, Mathematics Department, University of Chicago, US "If you have a pattern recognition problem, you should consider NETLAB; if you use NETLAB you must have this book." Keith Worden, University of Sheffield, UK
Posted in Computers