Symbolic Computation For Statistical Inference
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| Author | : David F. Andrews |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 184 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780198507055 |
Over recent years, developments in statistical computing have freed statisticians from the burden of calculation and have made possible new methods of analysis that previously would have been too difficult or time-consuming. Up till now these developments have been primarily in numerical computation and graphical display, but equal steps forward are now being made in the area of symbolic computing: the use of computer languages and procedures to manipulate expressions. This allows researchers to compute an algebraic expression, rather than evaluate the expression numerically over a given range. This book summarizes a decade of research into the use of symbolic computation applied to statistical inference problems. It shows the considerable potential of the subject to automate statistical calculation, leaving researchers free to concentrate on new concepts. Starting with the development of algorithms applied to standard undergraduate problems, the book then goes on to develop increasingly more powerful tools. Later chapters then discuss the application of these algorithms to different areas of statistical methodology.
| Author | : Christopher G. Small |
| Publisher | : Oxford University Press |
| Total Pages | : 330 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9780198506881 |
Non linearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihood's for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a number of modification to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student.
| Author | : D.R. Cox |
| Publisher | : CRC Press |
| Total Pages | : 181 |
| Release | : 2002-07-30 |
| Genre | : Mathematics |
| ISBN | : 1482285940 |
The components of variance is a notion essential to statisticians and quantitative research scientists working in a variety of fields, including the biological, genetic, health, industrial, and psychological sciences. Co-authored by Sir David Cox, the pre-eminent statistician in the field, this book provides in-depth discussions that set forth the essential principles of the subject. It focuses on developing the models that form the basis for detailed analyses as well as on the statistical techniques themselves. The authors include a variety of examples from areas such as clinical trial design, plant and animal breeding, industrial design, and psychometrics.
| Author | : P. Hitzler |
| Publisher | : IOS Press |
| Total Pages | : 410 |
| Release | : 2022-01-19 |
| Genre | : Computers |
| ISBN | : 1643682458 |
Neuro-symbolic AI is an emerging subfield of Artificial Intelligence that brings together two hitherto distinct approaches. ”Neuro” refers to the artificial neural networks prominent in machine learning, ”symbolic” refers to algorithmic processing on the level of meaningful symbols, prominent in knowledge representation. In the past, these two fields of AI have been largely separate, with very little crossover, but the so-called “third wave” of AI is now bringing them together. This book, Neuro-Symbolic Artificial Intelligence: The State of the Art, provides an overview of this development in AI. The two approaches differ significantly in terms of their strengths and weaknesses and, from a cognitive-science perspective, there is a question as to how a neural system can perform symbol manipulation, and how the representational differences between these two approaches can be bridged. The book presents 17 overview papers, all by authors who have made significant contributions in the past few years and starting with a historic overview first seen in 2016. With just seven months elapsed from invitation to authors to final copy, the book is as up-to-date as a published overview of this subject can be. Based on the editors’ own desire to understand the current state of the art, this book reflects the breadth and depth of the latest developments in neuro-symbolic AI, and will be of interest to students, researchers, and all those working in the field of Artificial Intelligence.
| Author | : Luigi Pace |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 557 |
| Release | : 1997-08-05 |
| Genre | : Mathematics |
| ISBN | : 9813103019 |
In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term “neo-Fisherian” highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.
| Author | : James E. Gentle |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1180 |
| Release | : 2012-07-06 |
| Genre | : Computers |
| ISBN | : 3642215513 |
The Handbook of Computational Statistics - Concepts and Methods (second edition) is a revision of the first edition published in 2004, and contains additional comments and updated information on the existing chapters, as well as three new chapters addressing recent work in the field of computational statistics. This new edition is divided into 4 parts in the same way as the first edition. It begins with "How Computational Statistics became the backbone of modern data science" (Ch.1): an overview of the field of Computational Statistics, how it emerged as a separate discipline, and how its own development mirrored that of hardware and software, including a discussion of current active research. The second part (Chs. 2 - 15) presents several topics in the supporting field of statistical computing. Emphasis is placed on the need for fast and accurate numerical algorithms, and some of the basic methodologies for transformation, database handling, high-dimensional data and graphics treatment are discussed. The third part (Chs. 16 - 33) focuses on statistical methodology. Special attention is given to smoothing, iterative procedures, simulation and visualization of multivariate data. Lastly, a set of selected applications (Chs. 34 - 38) like Bioinformatics, Medical Imaging, Finance, Econometrics and Network Intrusion Detection highlight the usefulness of computational statistics in real-world applications.
| Author | : Ronald Chrisley |
| Publisher | : Taylor & Francis |
| Total Pages | : 608 |
| Release | : 2000 |
| Genre | : Computers |
| ISBN | : 9780415193337 |
| Author | : Ernesto Damiani |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 267 |
| Release | : 2009-07-24 |
| Genre | : Computers |
| ISBN | : 0387887539 |
From Combinatorics to Philosophy: The Legacy of G. -C. Rota provides an assessment of G. -C. Rota's legacy to current international research issues in mathematics, philosophy and computer science. This volume includes chapters by leading researchers, as well as a number of invited research papers. Rota’s legacy connects European and Italian research communities to the USA by providing inspiration to several generations of researchers in combinatorics, philosophy and computer science. From Combinatorics to Philosophy: The Legacy of G. -C. Rota is of valuable interest to research institutions and university libraries worldwide. This book is also designed for advanced-level students in mathematics, computer science, and philosophy.
| Author | : Yimin Wei |
| Publisher | : World Scientific |
| Total Pages | : 470 |
| Release | : 2018-07-18 |
| Genre | : Mathematics |
| ISBN | : 9813238682 |
We introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed in other book, which is important for numerical-symbolic computations.
| Author | : John Haugeland |
| Publisher | : MIT Press |
| Total Pages | : 500 |
| Release | : 1997-03-06 |
| Genre | : Psychology |
| ISBN | : 9780262581530 |
Mind design is the endeavor to understand mind (thinking, intellect) in terms of its design (how it is built, how it works). Unlike traditional empirical psychology, it is more oriented toward the "how" than the "what." An experiment in mind design is more likely to be an attempt to build something and make it work—as in artificial intelligence—than to observe or analyze what already exists. Mind design is psychology by reverse engineering. When Mind Design was first published in 1981, it became a classic in the then-nascent fields of cognitive science and AI. This second edition retains four landmark essays from the first, adding to them one earlier milestone (Turing's "Computing Machinery and Intelligence") and eleven more recent articles about connectionism, dynamical systems, and symbolic versus nonsymbolic models. The contributors are divided about evenly between philosophers and scientists. Yet all are "philosophical" in that they address fundamental issues and concepts; and all are "scientific" in that they are technically sophisticated and concerned with concrete empirical research. Contributors Rodney A. Brooks, Paul M. Churchland, Andy Clark, Daniel C. Dennett, Hubert L. Dreyfus, Jerry A. Fodor, Joseph Garon, John Haugeland, Marvin Minsky, Allen Newell, Zenon W. Pylyshyn, William Ramsey, Jay F. Rosenberg, David E. Rumelhart, John R. Searle, Herbert A. Simon, Paul Smolensky, Stephen Stich, A.M. Turing, Timothy van Gelder
