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Author: Yonina C. Eldar Publisher: Now Publishers Inc ISBN: 1601981309 Category : Mathematics Languages : en Pages : 159
Book Description
Rethinking Biased Estimation discusses methods to improve the accuracy of unbiased estimators used in many signal processing problems. At the heart of the proposed methodology is the use of the mean-squared error (MSE) as the performance criteria. One of the prime goals of statistical estimation theory is the development of performance bounds when estimating parameters of interest in a given model, as well as constructing estimators that achieve these limits. When the parameters to be estimated are deterministic, a popular approach is to bound the MSE achievable within the class of unbiased estimators. Although it is well-known that lower MSE can be obtained by allowing for a bias, in applications it is typically unclear how to choose an appropriate bias. Rethinking Biased Estimation introduces MSE bounds that are lower than the unbiased Cramer-Rao bound (CRB) for all values of the unknowns. It then presents a general framework for constructing biased estimators with smaller MSE than the standard maximum-likelihood (ML) approach, regardless of the true unknown values. Specializing the results to the linear Gaussian model, it derives a class of estimators that dominate least-squares in terms of MSE. It also introduces methods for choosing regularization parameters in penalized ML estimators that outperform standard techniques such as cross validation.
Author: Yonina C. Eldar Publisher: Now Publishers Inc ISBN: 1601981309 Category : Mathematics Languages : en Pages : 159
Book Description
Rethinking Biased Estimation discusses methods to improve the accuracy of unbiased estimators used in many signal processing problems. At the heart of the proposed methodology is the use of the mean-squared error (MSE) as the performance criteria. One of the prime goals of statistical estimation theory is the development of performance bounds when estimating parameters of interest in a given model, as well as constructing estimators that achieve these limits. When the parameters to be estimated are deterministic, a popular approach is to bound the MSE achievable within the class of unbiased estimators. Although it is well-known that lower MSE can be obtained by allowing for a bias, in applications it is typically unclear how to choose an appropriate bias. Rethinking Biased Estimation introduces MSE bounds that are lower than the unbiased Cramer-Rao bound (CRB) for all values of the unknowns. It then presents a general framework for constructing biased estimators with smaller MSE than the standard maximum-likelihood (ML) approach, regardless of the true unknown values. Specializing the results to the linear Gaussian model, it derives a class of estimators that dominate least-squares in terms of MSE. It also introduces methods for choosing regularization parameters in penalized ML estimators that outperform standard techniques such as cross validation.
Author: Richard McElreath Publisher: CRC Press ISBN: 1315362619 Category : Mathematics Languages : en Pages : 488
Book Description
Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.
Author: Andrew Gelman Publisher: Cambridge University Press ISBN: 110702398X Category : Business & Economics Languages : en Pages : 551
Book Description
A practical approach to using regression and computation to solve real-world problems of estimation, prediction, and causal inference.
Author: Carsten Wehn Publisher: Academic Press ISBN: 0124158757 Category : Business & Economics Languages : en Pages : 658
Book Description
It is widely acknowledged that many financial modelling techniques failed during the financial crisis, and in our post-crisis environment many techniques are being reconsidered. This single volume provides a guide to lessons learned for practitioners and a reference for academics. Including reviews of traditional approaches, real examples, and case studies, contributors consider portfolio theory; methods for valuing equities and equity derivatives, interest rate derivatives, and hybrid products; and techniques for calculating risks and implementing investment strategies. Describing new approaches without losing sight of their classical antecedents, this collection of original articles presents a timely perspective on our post-crisis paradigm. Highlights pre-crisis best classical practices, identifies post-crisis key issues, and examines emerging approaches to solving those issues Singles out key factors one must consider when valuing or calculating risks in the post-crisis environment Presents material in a homogenous, practical, clear, and not overly technical manner
Author: Yonina C. Eldar Publisher: Cambridge University Press ISBN: 1316060594 Category : Technology & Engineering Languages : en Pages : 837
Book Description
Covering the fundamental mathematical underpinnings together with key principles and applications, this book provides a comprehensive guide to the theory and practice of sampling from an engineering perspective. Beginning with traditional ideas such as uniform sampling in shift-invariant spaces and working through to the more recent fields of compressed sensing and sub-Nyquist sampling, the key concepts are addressed in a unified and coherent way. Emphasis is given to applications in signal processing and communications, as well as hardware considerations, throughout. With 200 worked examples and over 200 end-of-chapter problems, this is an ideal course textbook for senior undergraduate and graduate students. It is also an invaluable reference or self-study guide for engineers and students across industry and academia.
Author: Reza Zekavat Publisher: John Wiley & Sons ISBN: 1118104765 Category : Science Languages : en Pages : 1138
Book Description
Radio systems capable of localization have emerging applications in homeland security, law enforcement, emergency response, defense command and control, multi-robot coordination and vehicle-to-vehicle and vehicle-to-pedestrian collision avoidance. In fact, high resolution localization is vital for many applications, including: traffic alert, emergency services, e.g., indoor localization for firefighters, and battlefield command and control. These systems promise to dramatically reduce society's vulnerabilities to catastrophic events and improve its quality of of life. While work this important area is progressing, limited resources are available to support graduate students and researchers in this important area. Specifically, a limited number of books has been published in this area covering selected subjects. This comprehensive handbook offers gaps of available localization books presenting in-depth coverage from fundamentals of coordinates to advanced application examples.
Author: Benjamin Smith Publisher: Cambridge University Press ISBN: 1108788033 Category : Political Science Languages : en Pages : 156
Book Description
This Element documents the diversity and dissensus of scholarship on the political resource curse, diagnoses its sources, and directs scholarly attention towards what the authors believe will be more fruitful avenues of future research. In the scholarship to date, there is substantial regional heterogeneity and substantial evidence denying the existence of a political resource curse. This dissensus is located in theory, measure, and research design, especially regarding measurement error and endogenous selection. The work then turns to strategies for reconnecting research on resource politics to the broader literature on democratic development. Finally, the results of the authors' own research is presented, showing that a set of historically contingent events in the Middle East and North Africa are at the root of what has been mistaken for a global political resource curse.
Author: Yonina C. Eldar Publisher: Cambridge University Press ISBN: 1107394392 Category : Technology & Engineering Languages : en Pages : 557
Book Description
Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on computer vision, coding theory, signal processing, image processing and algorithms for efficient data processing.
Author: Paulo S. R. Diniz Publisher: Cambridge University Press ISBN: 1139491571 Category : Technology & Engineering Languages : en Pages : 913
Book Description
This new, fully-revised edition covers all the major topics of digital signal processing (DSP) design and analysis in a single, all-inclusive volume, interweaving theory with real-world examples and design trade-offs. Building on the success of the original, this edition includes new material on random signal processing, a new chapter on spectral estimation, greatly expanded coverage of filter banks and wavelets, and new material on the solution of difference equations. Additional steps in mathematical derivations make them easier to follow, and an important new feature is the do-it-yourself section at the end of each chapter, where readers get hands-on experience of solving practical signal processing problems in a range of MATLAB experiments. With 120 worked examples, 20 case studies, and almost 400 homework exercises, the book is essential reading for anyone taking DSP courses. Its unique blend of theory and real-world practical examples also makes it an ideal reference for practitioners.
Author: Yonina C. Eldar
Author: Yonina C. Eldar
Author: Richard McElreath
Author: Andrew Gelman
Author: Carsten Wehn
Author: Yonina C. Eldar
Author: Reza Zekavat
Author: Douglas J. Besharov
Author: Benjamin Smith
Author: Yonina C. Eldar
Author: Paulo S. R. Diniz