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Maximum-Likelihood Deconvolution: A Journey into Model-Based Signal Processing (Signal Processing and Digital Filtering)
Jerry M. Mendel
Manufacturer: Springer
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ASIN: 0387972080 |
Book Description
Convolution is the most important operation that describes the behavior of a linear time-invariant dynamical system. Deconvolution is the unraveling of convolution. It is the inverse problem of generating the system's input from knowledge about the system's output and dynamics. Deconvolution requires a careful balancing of bandwidth and signal-to-noise ratio effects. Maximum-likelihood deconvolution (MLD) is a design procedure that handles both effects. It draws upon ideas from Maximum Likelihood, when unknown parameters are random. It leads to linear and nonlinear signal processors that provide high-resolution estimates of a system's input. All aspects of MLD are described, from first principles in this book. The purpose of this volume is to explain MLD as simply as possible. To do this, the entire theory of MLD is presented in terms of a convolutional signal generating model and some relatively simple ideas from optimization theory. Earlier approaches to MLD, which are couched in the language of state-variable models and estimation theory, are unnecessary to understand the essence of MLD. MLD is a model-based signal processing procedure, because it is based on a signal model, namely the convolutional model. The book focuses on three aspects of MLD: (1) specification of a probability model for the system's measured output; (2) determination of an appropriate likelihood function; and (3) maximization of that likelihood function. Many practical algorithms are obtained. Computational aspects of MLD are described in great detail. Extensive simulations are provided, including real data applications.
Book Description
Econometric Modeling provides a new and stimulating introduction to econometrics, focusing on modeling. The key issue confronting empirical economics is to establish sustainable relationships that are both supported by data and interpretable from economic theory. The unified likelihood-based approach of this book gives students the required statistical foundations of estimation and inference, and leads to a thorough understanding of econometric techniques.
David Hendry and Bent Nielsen introduce modeling for a range of situations, including binary data sets, multiple regression, and cointegrated systems. In each setting, a statistical model is constructed to explain the observed variation in the data, with estimation and inference based on the likelihood function. Substantive issues are always addressed, showing how both statistical and economic assumptions can be tested and empirical results interpreted. Important empirical problems such as structural breaks, forecasting, and model selection are covered, and Monte Carlo simulation is explained and applied.
Econometric Modeling is a self-contained introduction for advanced undergraduate or graduate students. Throughout, data illustrate and motivate the approach, and are available for computer-based teaching. Technical issues from probability theory and statistical theory are introduced only as needed. Nevertheless, the approach is rigorous, emphasizing the coherent formulation, estimation, and evaluation of econometric models relevant for empirical research.
Book Description
Since their introduction in 1972, generalized linear models (GLMs) have proven useful in the generalization of classical normal models. Presenting methods for fitting GLMs with random effects to data, Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood explores a wide range of applications, including combining information over trials (meta-analysis), analysis of frailty models for survival data, genetic epidemiology, and analysis of spatial and temporal models with correlated errors. Written by pioneering authorities in the field, this reference provides an introduction to various theories and examines likelihood inference and GLMs. The authors show how to extend the class of GLMs while retaining as much simplicity as possible. By maximizing and deriving other quantities from h-likelihood, they also demonstrate how to use a single algorithm for all members of the class, resulting in a faster algorithm as compared to existing alternatives. Complementing theory with examples, many of which can be run by using the code supplied on the accompanying CD, this book is beneficial to statisticians and researchers involved in the above applications as well as quality-improvement experiments and missing-data analysis.
Book Description
Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.
Customer Reviews:
In All Likelihood: Statistical Modelling and Inference Using Likelihood.......2006-05-13
I give the book 5 stars, meaning excellent at what it sets out to accomplish. It is one of the few books that does a sound job of integrating statistical theory and statistical practice. Not meant to be a first course in statistics, but probably excellent for a third or fourth course. The student should probably have had a year long course in mathematical statistics and an introduction to statistical computing in R with linear models. After all, the book is focused on likelihood based statistical inference. I should note that the book is stresses integrating statistical ideas and statistical thinking, it is not a mathematical statistics text. The text contains a number of topics (18 chapters) and should be of interest to anyone who wishes to be a competent applied statistician. Any student who has had a year with Mood & Graybill, "Introduction to the Theory of Statistics", and a year with "Statistical Models" by A.C. Davison, will be ready to appreciate "In All Likelihood". Any student who has all three of these courses will have a fundamental understanding of statistical inference and what it means to be an applied statistician. They will also achieve this in the shortest, most direct path.
Statistical Modelling and Inference for this Century.......2004-05-30
I used "In All Likelihood" as a basis for the 13 week 3rd year Mathematical Statistics/ Statistical Inference course I have almost finished teaching. Finding this book at Amazon was my very good fortune. It is exactly the way I would have tried to write such a course but I couldn't have done as good a job as Pawitan.
I like this book because it covers all the theory, such as, sufficiency, completeness, minimum variance unbiased estimation, large sample asymptotics etc. But the beauty of the book lies in the relevant, modern examples. Likelihood functions are liberally graphed for the many examples. These are created in R; if you are an R user, or wish to be, you'll like the availability of the source code. If you're not into R, it won't make a difference to the usability of the book.
Books like Bickel & Doksum, Casella & Berger and Rice, have the theory, but not the range of practical examples that add so much to "In All Likelihood". Pawitan's theoretical sections are comparatively easy to follow. Pawitan points out important results rather than the reader needing to surmise what bits of theory are useful in practice.
On the other hand, since reading Pawitan I can now read sections out of McCullough and Nelder, and other applications books, no longer feeling I have missed some important background theory.
I see signs of good teaching practice throughout "In All Likelihood" that make it easy to learn and teach from. For example, difficult concepts are often initially introduced in an example and then reintroduced in technical detail. This way the learner feels some familiarity the second time around.
Semester is nearly over. We covered the first nine chapters (out of 18) in 38 hours of lectures. I'm reading the rest of the book now. Every page or two something else I have heard, seen or read in the past begins to make more sense. Examples of topics in the second half of the book are the EM algorithm, Generalized Estimating Equations and random/mixed effects models. I told my students that if they considered buying a book for their future in statistics, "In All Likelihood" is a very good one.
Book Description
Written by the creators of Stata's likelihood maximization features, Maximum Likelihood Estimation with Stata, Third Edition continues the pioneering work of the previous editions. Emphasizing practical implications for applied work, the first chapter provides an overview of maximum likelihood estimation theory and numerical optimization methods. With step-by-step instructions, the next several chapters detail the use of Stata to maximize user-written likelihood functions. Various examples include logit, probit, linear, Weibull, and random-effects linear regression as well as the Cox proportional hazards model. The final chapters describe how to add a new estimation command to Stata. Assuming a familiarity with Stata, this reference is ideal for researchers who need to maximize their own likelihood functions. New ml commands and their functions: · constraint: fits a model with linear constraints on the coefficient by defining your constraints; accepts a constraint matrix · ml model: picks up survey characteristics; accepts the subpop option for analyzing survey data · optimization algorithms: Berndt-Hall-Hall-Hausman (BHHH), Davidon-Fletcher-Powell (DFP), Broyden-Fletcher-Goldfarb-Shanno (BFGS) · ml: switches between optimization algorithms; computes variance estimates using the outer product of gradients (OPG)
Product Description
Get a solid, hands-on grasp of all the essential factors used by the courts to determine if likelihood of confusion exists in trademark disputes, including full step-by-step coverage of the dominant multiple-factor test. Likelihood of Confusion in Trademark Law enables you to conduct effective trademark searches and avoid disputes -- establish the strength of a mark -- prove actual confusion -- add features to make marks truly distinctive -- prove rightful intent for junior users -- and more - all with the aid of checklists and hundreds of defining examples.
Customer Reviews:
Commentary on LIkelihood of Confusion by Kirkpatrick.......2006-08-11
Amazing. Anything, and everything an attorney, or even non-attorney, would want and need to know. Presented in articulate, organized fashion. Must-have for anybody looking into Trademark Law questions/issues/consideration.
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Likelihood, Bayesian and MCMC Methods in Quantitative Genetics
Daniel Sorensen , and
Daniel Gianola
Manufacturer: Springer
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ASIN: 0387954406 |
Book Description
Over the last ten years the introduction of computer intensive statistical methods has opened new horizons concerning the probability models that can be fitted to genetic data, the scale of the problems that can be tackled and the nature of the questions that can be posed. In particular, the application of Bayesian and likelihood methods to statistical genetics has been facilitated enormously by these methods. Techniques generally referred to as Markov chain Monte Carlo (MCMC) have played a major role in this process, stimulating synergies among scientists in different fields, such as mathematicians, probabilists, statisticians, computer scientists and statistical geneticists. Specifically, the MCMC "revolution" has made a deep impact in quantitative genetics. This can be seen, for example, in the vast number of papers dealing with complex hierarchical models and models for detection of genes affecting quantitative or meristic traits in plants, animals and humans that have been published recently. This book, suitable for numerate biologists and for applied statisticians, provides the foundations of likelihood, Bayesian and MCMC methods in the context of genetic analysis of quantitative traits. Most students in biology and agriculture lack the formal background needed to learn these modern biometrical techniques. Although a number of excellent texts in these areas have become available in recent years, the basic ideas and tools are typically described in a technically demanding style, and have been written by and addressed to professional statisticians. For this reason, considerable more detail is offered than what may be warranted for a more mathematically apt audience. The book is divided into four parts. Part I gives a review of probability and distribution theory. Parts II and III present methods of inference and MCMC methods. Part IV discusses several models that can be applied in quantitative genetics, primarily from a Bayesian perspective. An effort has been made to relate biological to statistical parameters throughout, and examples are used profusely to motivate the developments. Daniel Sorensen is a Research Professor in Statistical Genetics, at the Department of Animal Breeding and Genetics in the Danish Institute of Agricultural Sciences. Daniel Gianola is Professor in the Animal Sciences, Biostatistics and Medical Informatics, and Dairy Science Departments of the University of Wisconsin-Madison. Gianola and Sorensen pioneered the introduction of Bayesian and MCMC methods in animal breeding. The authors have published and lectured extensively in applications of statistics to quantitative genetics.
Customer Reviews:
Highly recommended!.......2004-08-27
This book contains a wealth of well presented and organized information, which is not easy to find in texts of similar level. I especially enjoyed the style and clarity of presentation. Outstanding!
Book Description
Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It also facilitates incorporating side information, and it simplifies accounting for censored, truncated, or biased sampling. One of the first books published on the subject, Empirical Likelihood offers an in-depth treatment of this method for constructing confidence regions and testing hypotheses. The author applies empirical likelihood to a range of problems, from those as simple as setting a confidence region for a univariate mean under IID sampling, to problems defined through smooth functions of means, regression models, generalized linear models, estimating equations, or kernel smooths, and to sampling with non-identically distributed data. Abundant figures offer visual reinforcement of the concepts and techniques. Examples from a variety of disciplines and detailed descriptions of algorithms-also posted on a companion Web site at-illustrate the methods in practice. Exercises help readers to understand and apply the methods. The method of empirical likelihood is now attracting serious attention from researchers in econometrics and biostatistics, as well as from statisticians. This book is your opportunity to explore its foundations, its advantages, and its application to a myriad of practical problems.
Customer Reviews:
Destined to be a classic.......2001-08-23
This book will make accessible to a wider audience the new and important area of nonparameteric likelihood and hypothesis testing. It is written by a pioneer in this area. The ideas in this book are very sophisticated but one has no difficulty following the arguments because the writing is crystal clear; the author must have put in a lot of thought into the organization and presentation of the ideas. The book lucidly discusses the statistical theory and -- perhaps more importantly for the practitioner -- computational details and practical aspects of putting the ideas to work with real data. I expect that this book will have a major impact on the way hypothesis testing is done in econometrics and other areas of applied statistics, where one is very often unsure about what the correct model specification is and cannot rely on certain large sample approximations. A terrific book. I would recommend it very highly to practitioners in areas where hypothesis testing is too important to be left to less correct approaches (I am thinking of areas like biostatistics, quality control, econometrics, but I expect there are many such areas).
Book Description
This book provides an introduction to the modern theory of likelihood-based statistical inference. This theory is characterized by several important features. One is the recognition that it is desirable to condition on relevant ancillary statistics. Another is that probability approximations are based on saddlepoint and closely related approximations that generally have very high accuracy. A third aspect is that, for models with nuisance parameters, inference is often based on marginal or conditional likelihoods, or approximations to these likelihoods. These methods have been shown often to yield substantial improvements over classical methods. The book also provides an up-to-date account of recent results in the field, which has been undergoing rapid development.
Book Description
"
Maximum Likelihood Estimation. . . provides a useful introduction. . . it is clear and easy to follow with applications and graphs. . . . I consider this a very useful book. . . . well-written, with a wealth of explanation. . ."
--Dougal Hutchison in Educational Research
Eliason reveals to the reader the underlying logic and practice of maximum likelihood (ML) estimation by providing a general modeling framework that utilizes the tools of ML methods. This framework offers readers a flexible modeling strategy since it accommodates cases from the simplest linear models (such as the normal error regression model) to the most complex nonlinear models that link a system of endogenous and exogenous variables with non-normal distributions. Using examples to illustrate the techniques of finding ML estimators and estimates, Eliason discusses what properties are desirable in an estimator, basic techniques for finding maximum likelihood solutions, the general form of the covariance matrix for ML estimates, the sampling distribution of ML estimators; the use of ML in the normal as well as other distributions, and some useful illustrations of likelihoods.
Customer Reviews:
Has some value.......2003-12-01
The first step in common applications of probability is to figure out what distribution to use. That depends on the structure of your problem, and is up to you. This book helps with the second step: figuring out what set of values for that distribution's parameters give the best fit to your data.
It was certainly interesting to see least squares regression derived using ML, instead of the usual geometric interpretation. It was quite worthwhile to see a mutual dependence metric that works when normal "correlation" doesn't. It also broadened my view, a little, to see standard linear and non-linear solution techniques in a different notation than usual.
As you can see by the breadth of topics in this slim (82-page) book, the author covers a good bit of territory tangential to ML - in a larger book, that could have turned into a serious organization problem. About 10 of the book's pages give sample code in the Gauss language. That language isn't in the main stream of engineering computing, but a Matlab or Mathematica user can read it easily enough.
I did learn a few useful things from this book - I won't be giving it away. It probably won't suit either the beginner in statistics or the specialist, though. If you're in the middle, like me, it has modest value.
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