Book Description
Statistics lectures have been a source of much bewilderment and frustration for generations of students. This book attempts to remedy the situation by expounding a logical and unified approach to the whole subject of data analysis.
This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image
processing. Other topics covered include reliability analysis, multivariate optimization, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimental design.
The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical technique
for Bayesian computation called 'nested sampling'.
Customer Reviews:
In-Depth and Practical.......2007-08-03
Sivia and Skilling give a concise and clear exposition of Bayesian statistical analysis, and pair it with practical, real examples. It has been a great aid to me in doing actual data work. This text gets the balance of theoretical detail and practicality just right. In particular, abandoning the usual emphasis on analytical solutions and instead pairing real examples with numerical solution algorithms when appropriate, is perfect for someone concerned with applying Bayesian statistical analysis to real problems. A great and genuinely useful book!
Book Description
Statistics lectures have often been viewed with trepidation by engineering and science students taking an ancillary course in this subject. Whereas there are many texts showing "how" statistical methods are applied, few provide a clear explanation for non-statisticians of how the principles of data analysis can be based on probability theory. Data Analysis: A Bayesian Tutorial provides such a text, putting emphasis as much on understanding "why" and "when" certain statistical procedures should be used as "how". This difference in approach makes the text ideal as a tutorial guide for senior undergraduates and research students, in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. With its central emphasis on a few fundamental rules, this book takes the mystery out of statistics by providing a clear rationale for some of the most widely-used procedures.
Customer Reviews:
concise but clear.......2006-03-06
Sivia offers a brief but thorough explanation of how to use Bayesians in data analysis. He illustrates with important examples that commonly often arise in the sciences. As in estimating the true amplitude of a signal in the presence of background noise. These days, for anyone in a lab sitting next to an electronic gadget acquiring data, you can surely emphathise with this problem.
The necessary background for his book includes being familiar with multivariable calculus. Specifically, with the Taylor expansion in several variables, and with the Jacobian matrix of second partial derivatives. Plus of course a grounding in statistics, including maximum likelihood estimations and the normal distribution.
A gem........2005-12-05
This tutorial on Bayesian data analysis is a gem: very terse, yet explaining the concepts very clearly, giving many insightful examples along the way. This is achieved within only 180 pages by focussing on understanding and intuition instead of mathematical formalism. After reading this tutorial, the reader will be familiar with the way of thinking in Bayesian statistics. The tutorial thus encourages the reader to get more independent from the (conceptually more complicated) cook book statistics with the associated risk of misusage. When reading this book I felt as if a whole jumble of more or less unconnected pieces of statistical wisdom was finally falling into place within the Bayesian framework.
A few critical remarks: (1) A clearer structure with more informative section and subsection headings would help to quicker find things and keep the material orderly in one`s mind. (As an example, the two core chapters are entitled Parameter estimation I" and Parameter estimation II"). (2) The chapter on non-paramteric estimation is much harder to understand than the first six chapters. This is in part justified by the advancedness of the topic but it could profit from a streamlining (and updating). (3) This book certainly would have the chance to become much more popular than it is now if it was more reasonably priced.
The reader should have a firm command of elementary probability theory, first year calculus (Taylor expansion, multidimensional integration, finding the maximum of a multi-variable function), as well as elementary linear algebra (diagonalization, eigenvectors, determinants). Ideally, she should be familiar with basic classical statistics, as this will make her appreciate the elegance of the Bayesian view more. Physicists will love this book.
Bayes' Theorem made simple.......2004-10-02
This is an excellent tutorial for the both the beginner (undergraduate) and more advanced scientist. Sivia takes the reader through several examples with simple and concise explanations. I have used many of the examples discussed in the book as starting points for problems that I have encountered in my work. I would recommend giving it a try...
Learn what it means to be a "Bayesian".......2004-09-15
For years I listened to people present "Bayesian" solutions to problems without appreciating the subtler implications of the term. Bayes' theorem is one of the first topics taught in freshman-level probability and statistics. It's taught, and it's used, but it isn't a central part of the teaching of modern statistics.
Bayesians make it central. Sivia does a masterful job of deriving most of statistics from judicious applications of Bayes' theorem. He can do this, in part, because the visible universe is finite. Infinities and limit theorems can be bypassed, and previously impossible functional forms become workable.
The book is a tutorial; you have to think. But it's well worth it.
poor pedagogy.......2004-01-17
Maybe it's just me but I found this book not very helpful. The easy stuff is repeated often (Bayes's theorem is quoted every few pages) but when a difficulty arises it is glossed over. Maybe it gets better: I decided not to finish the book.
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Bayesian Inference and Maximum Entropy Methods in Science and Engineering: 26th International Workshop on Bayesian Inference and Maximum Entropy Methods ... / Mathematical and Statistical Phsyics)
Manufacturer: American Institute of Physics
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ASIN: 0735403716 |
Book Description
All papers have been peer-reviewed. The MaxEnt workshops are devoted to Bayesian inference and maximum entropy methods in science and engineering. In addition, this workshop included all aspects of probabilistic inference, such as foundations, techniques, algorithms, and applications. Specific topics included are: information theory; probability theory; quantum systems; source separation; information geometry; Bayesian networks, parametric and non-parametric Bayesian data and image processing; Bayesian computation; entropy computation of Markovian and semi-Markovian processes.
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The Maximum Entropy Method (Springer Series in Information Sciences)
Nailong Wu
Manufacturer: Springer-Verlag Telos
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ASIN: 3540619658 |
Book Description
The Maximum Entropy Method (MEM) has its roots in the Principle of Maximum Entropy introduced by Jaynes into the field of statistical mechanics almost 40 years ago. This principle has since been adopted in many areas of science and technology, such as spectral analysis and image restoration. This monograph consists of five chapters and two appendices. The first three chapters are devoted to MEM and its applications in spectral analysis and image restoration, including algrorithms in practical use. Chapter 4 is concerned with experimental and theoretical analysis and comparison of the basic ideas, and properties and applications of MEM. Chapter 5 presents MEM in mathematics and physics. The appendices provide relevant details of cepstral analysis and image restoration.
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- Top of my list
- Excellent treatise for ecologists
- Excellent reference for spatial-temporal statistics
- Truly important book
- Fresh Air in Geostatistics
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Modern Spatiotemporal Geostatistics (Studies in Mathematical Geology, 6.)
George Christakos
Manufacturer: Oxford University Press, USA
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Random Field Models in Earth Sciences (Dover Books on Science)
ASIN: 0195138953 |
Book Description
It is widely recognized that the techniques of classical geostatistics, which have been used for several decades, have reached their limit, and the time has come for some alternative approaches to be given a chance. This book, therefore, is an introduction to the fundamentals of modern geostatistics, which is a group of spatiotemporal concepts and methods that are the products of the advancement of the epistemic status of stochastic data analysis. The latter is considered from a novel perspective, promoting the view that a deeper understanding of a theory of knowledge is an important prerequisite for the development of improved mathematical models of scientific mapping. The main focus of the book is the Bayesian Maximum Entropy (BME) approach for studying spatiotemporal distributions of natural variables. As part of the modern geostatistics paradigm, the BME approach provides a fundamental insight into the mapping problem in which the knowledge of a natural variable, not the variable itself, is the direct object of study. The thread running throughout the book is that the modern geostatistical approach to environmental problems is that of natural scientists who are more interested in a stochastic analysis concerned with both the ontological level(building models for physical systems) and the epistemic level (using what we know about the physical systems and integrating and modeling knowledge from a variety of scientific disciplines), rather than in the pure naive inductive account of science based merely on a linear relationship between data and hypotheses and theory-free techniques that may be useful in other areas.
Customer Reviews:
Top of my list.......2005-10-12
Usually I am hesitant to write a review until I use a book for a year or more. I did that and now can say. This is the best geostat book ever written. Period!!! Ignore the ridiculous oldtimers and underachievers who never published anything new and correct, and who lost the ground under their feet when this book appeared, and get the book.
Excellent treatise for ecologists.......2004-04-17
This book is an advanced treatise on spatial-temporal geostatistics. It includes many ideas and techniques which are very useful for ecologic modelers. Its mathematics kind of tough for some ecologists but necessary for advanced analyses, so worth the investment. I find the methods of treatise very suitable for spatial-temporal ecological studies, for which seems to be a perfect model. I suggest all ecologic modelers have a look at the treatise. I wish it is translated in Russian.
Excellent reference for spatial-temporal statistics.......2004-02-16
I found the book very interesting for my research objectives. It is a valuable source of fundamental theory as well as a source of spatial-temporal statistics applied in real-world problems. I do not know of any other book that is so complete as this one.
Truly important book.......2003-11-02
This book is a truly important contribution to the field of space and time analysis, with a host of applications in epidemiology, geography and biology. It introduces an innovative approach, completely different from previous approaches one finds in the life sciences' literature. As a result, spatial and time analysis is boring no more. I used the book in my course last year and the students got a lot out of it, even some ideas for doctoral research. Unfortunately, the book is out of print, already, and the publisher should have new print so that students do not have to pay 3 times its original value to get it used (!).
Fresh Air in Geostatistics.......2003-10-16
This is a book that the geostatistics community needed desperately. It seems to be the first major development since the publication of Matheron's classic, almost 40 years ago. The book has many novel ideas and techniques, which open new and exciting avenues in geostatistics and spatial-temporal statistics research. I find that among the most important contributions of this book are: The geostatistical approach presented is based on solid physical science reasoning rather than the usual data massaging techniques. Fascinating links are established between geostatistics and other fields, like stochastic mathematics, image processing, mapping science, geographical systems, natural sciences, environmental assessment, human exposure and cognitive science. The connection of geostatistics with epistemology and the theory of knowledge is brilliant, and this is one more original feature of the book's approach. Also, the connection with the stochastic differential equations theory is most appropriate, given that most physical laws are expressed in terms of such equations. I gained lots of respect for geostatistics after reading this book --highly recommended.
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Maximum Entropy and Bayesian Methods Garching, Germany 1998 (Fundamental Theories of Physics)
Manufacturer: Springer
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ASIN: 0792357663 |
Book Description
This volume, arising from the 1998 MaxEnt conference, contains a wide range of applications of Bayesian probability theory and maximum entropy methods to problems of concern in such fields as physics, image processing, coding theory, machine learning, economics, data analysis and various other problems. It presents papers by the leading researchers in the field of Bayesian statistics and maximum entropy methods, and represents the latest developments in the field.
Audience: This book will be of interest to researchers in applied statistics, information theory, coding theory, image and signal processing.
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Maximum Entropy and Bayesian Methods (Fundamental Theories of Physics)
Manufacturer: Springer
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ASIN: 0792302249 |
Book Description
This volume records the proceedings of the Fourteenth International Workshop on Maximum Entropy and Bayesian Methods, held in Cambridge, England from August 1-5, 1994.
Throughout applied science, Bayesian inference is giving high quality results augmented with reliabilities in the form of probability values and probabilistic error bars. Maximum Entropy, with its emphasis on optimally selected results, is an important part of this. Across wide areas of spectroscopy and imagery, it is now realistic to generate clear results with quantified reliability. This power is underpinned with a foundation of solid mathematics.
The annual Maximum Entropy Workshops have become the principal focus of developments in the field, and which capture the imaginative research that defines the state of the art in the subject. The breadth of application is seen in the thirty-three papers reproduced here, which are classified into subsections on Basics, Applications, Physics and Neural Networks.
Audience: This volume will be of interest to graduate students and researchers whose work involves probability theory, neural networks, spectroscopic methods, statistical thermodynamics and image processing.
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Maximum Entropy and Bayesian Methods in Inverse Problems (Fundamental Theories of Physics)
Manufacturer: Springer
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ASIN: 9027720746 |
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Maximum Entropy in Action: A Collection of Expository Essays (Oxford Science Publications)
Manufacturer: Oxford University Press, USA
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Probability Theory: The Logic of Science
ASIN: 0198539630 |
Book Description
The powerful new technique of maximum entropy, which has its roots in probability theory, provides a much needed extension of the established principles of rational inference in the sciences. It allows the interpretation of incomplete and noisy data, to provide a description of the underlying physical system, and has found application in both practical and theoretical studies ranging form image enhancement to nuclear physics, from statistical mechanics to economics. This book is a diverse collection of introductory articles based on a series of interdisciplinary lectures covering the fundamentals of the maximum entropy approach and Bayesian methods, as well as the application of the method to various problems of data analysis in the physical sciences.
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Maximum Entropy Econometrics: Robust Estimation with Limited Data
Amos Golan
Manufacturer: John Wiley & Sons
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ASIN: 0471953113 |
Book Description
In the theory and practice of econometrics the model, the method and the data are all interdependent links in information recovery-estimation and inference. Seldom, however, are the economic and statistical models correctly specified, the data complete or capable of being replicated, the estimation rules optimal and the inferences free of distortion. Faced with these problems, Maximum Entropy Economeirics provides a new basis for learning from economic and statistical models that may be non-regular in the sense that they are ill-posed or underdetermined and the data are partial or incomplete. By extending the maximum entropy formalisms used in the physical sciences, the authors present a new set of generalized entropy techniques designed to recover information about economic systems. The authors compare the generalized entropy techniques with the performance of the relevant traditional methods of information recovery and clearly demonstrate theories with applications including
- Pure inverse problems that include first order Markov processes, and input-output, multisectoral or SAM models to
- Inverse problems with noise that include statistical models subject to ill-conditioning, non-normal errors, heteroskedasticity, autocorrelation, censored, multinomial and simultaneous response data, as well as model selection and non-stationary and dynamic control problems
Maximum Entropy Econometrics will be of interest to econometricians trying to devise procedures for recovering information from partial or incomplete data, as well as quantitative economists in finance and business, statisticians, and students and applied researchers in econometrics, engineering and the physical sciences.
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