The Theory Of Inference

Author : David J. C. MacKay
Publisher : Cambridge University Press
Page : 694 pages
File Size : 43,5 Mb
Release : 2003-09-25
Category : Computers
ISBN : 0521642981

Get Book

Information Theory, Inference and Learning Algorithms by David J. C. MacKay Pdf

Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.

Author : David J. Olive
Publisher : Springer
Page : 438 pages
File Size : 48,5 Mb
Release : 2014-05-07
Category : Mathematics
ISBN : 9783319049724

Get Book

Statistical Theory and Inference by David J. Olive Pdf

This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.

Author : Henry Hughes
Publisher : Unknown
Page : 280 pages
File Size : 42,9 Mb
Release : 1894
Category : Inference
ISBN : UOM:39015011378497

Get Book

The Theory of Inference by Henry Hughes Pdf

Author : Hannelore Liero,Silvelyn Zwanzig
Publisher : CRC Press
Page : 280 pages
File Size : 53,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466503205

Get Book

Introduction to the Theory of Statistical Inference by Hannelore Liero,Silvelyn Zwanzig Pdf

Based on the authors' lecture notes, this text presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Unlike related textbooks, it combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models. Suitable for a second semester undergraduate course on statistical inference, the text offers proofs to support the mathematics and does not require any use of measure theory. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

Author : Hughes Henry
Publisher : Hardpress Publishing
Page : 286 pages
File Size : 46,9 Mb
Release : 2013-06
Category : Electronic
ISBN : 1314520873

Get Book

The Theory of Inference by Hughes Henry Pdf

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Author : Gary King
Publisher : University of Michigan Press
Page : 290 pages
File Size : 40,8 Mb
Release : 1998-06-24
Category : Mathematics
ISBN : 0472085549

Get Book

Unifying Political Methodology by Gary King Pdf

DIVArgues that likelihood theory is a unifying approach to statistical modeling in political science /div

Author : Masanobu Taniguchi,Yoshihide Kakizawa
Publisher : Springer Science & Business Media
Page : 671 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211624

Get Book

Asymptotic Theory of Statistical Inference for Time Series by Masanobu Taniguchi,Yoshihide Kakizawa Pdf

The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

Author : Henry Hughes
Publisher : Unknown
Page : 284 pages
File Size : 47,9 Mb
Release : 1894
Category : Inference
ISBN : UCAL:B3928071

Get Book

The Theory of Inference by Henry Hughes Pdf

Author : Jaakko Hintikka,Patrick Suppes
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401032964

Get Book

Information and Inference by Jaakko Hintikka,Patrick Suppes Pdf

In the last 25 years, the concept of information has played a crucial role in communication theory, so much so that the terms information theory and communication theory are sometimes used almost interchangeably. It seems to us, however, that the notion of information is also destined to render valuable services to the student of induction and probability, of learning and reinforcement, of semantic meaning and deductive inference, as~well as of scientific method in general. The present volume is an attempt to illustrate some of these uses of information concepts. In 'On Semantic Information' Hintikka summarizes some of his and his associates' recent work on information and induction, and comments briefly on its philosophical suggestions. Jamison surveys from the sub jectivistic point of view some recent results in 'Bayesian Information Usage'. Rosenkrantz analyzes the information obtained by experimen tation from the Bayesian and Neyman-Pearson standpoints, and also from the standpoint of entropy and related concepts. The much-debated principle of total evidence prompts Hilpinen to examine the problem of measuring the information yield of observations in his paper 'On the Information Provided by Observations'. Pietarinen addresses himself to the more general task of evaluating the systematizing ('explanatory') power of hypotheses and theories, a task which quickly leads him to information concepts. Domotor develops a qualitative theory of information and entropy. His paper gives what is probably the first axiomatization of a general qualitative theory of information adequate to guarantee a numerical representation of the standard sort.

Author : Kenneth I. Wolpin
Publisher : MIT Press
Page : 197 pages
File Size : 43,6 Mb
Release : 2013-04-26
Category : Business & Economics
ISBN : 9780262019088

Get Book

The Limits of Inference without Theory by Kenneth I. Wolpin Pdf

The role of theory in ex ante policy evaluations and the limits that eschewing theory places on inference In this rigorous and well-crafted work, Kenneth Wolpin examines the role of theory in inferential empirical work in economics and the social sciences in general—that is, any research that uses raw data to go beyond the mere statement of fact or the tabulation of statistics. He considers in particular the limits that eschewing the use of theory places on inference. Wolpin finds that the absence of theory in inferential work that addresses microeconomic issues is pervasive. That theory is unnecessary for inference is exemplified by the expression “let the data speak for themselves.” This approach is often called “reduced form.” A more nuanced view is based on the use of experiments or quasi-experiments to draw inferences. Atheoretical approaches stand in contrast to what is known as the structuralist approach, which requires that a researcher specify an explicit model of economic behavior—that is, a theory. Wolpin offers a rigorous examination of both structuralist and nonstructuralist approaches. He first considers ex ante policy evaluation, highlighting the role of theory in the implementation of parametric and nonparametric estimation strategies. He illustrates these strategies with two examples, a wage tax and a school attendance subsidy, and summarizes the results from applications. He then presents a number of examples that illustrate the limits of inference without theory: the effect of unemployment benefits on unemployment duration; the effect of public welfare on women's labor market and demographic outcomes; the effect of school attainment on earnings; and a famous field experiment in education dealing with class size. Placing each example within the context of the broader literature, he contrasts them to recent work that relies on theory for inference.

Author : Anthony Almudevar
Publisher : CRC Press
Page : 470 pages
File Size : 50,5 Mb
Release : 2021-12-30
Category : Mathematics
ISBN : 9781000488012

Get Book

Theory of Statistical Inference by Anthony Almudevar Pdf

Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.

Author : Thomas Parr,Giovanni Pezzulo,Karl J. Friston
Publisher : MIT Press
Page : 313 pages
File Size : 51,9 Mb
Release : 2022-03-29
Category : Science
ISBN : 9780262362283

Get Book

Active Inference by Thomas Parr,Giovanni Pezzulo,Karl J. Friston Pdf

The first comprehensive treatment of active inference, an integrative perspective on brain, cognition, and behavior used across multiple disciplines. Active inference is a way of understanding sentient behavior—a theory that characterizes perception, planning, and action in terms of probabilistic inference. Developed by theoretical neuroscientist Karl Friston over years of groundbreaking research, active inference provides an integrated perspective on brain, cognition, and behavior that is increasingly used across multiple disciplines including neuroscience, psychology, and philosophy. Active inference puts the action into perception. This book offers the first comprehensive treatment of active inference, covering theory, applications, and cognitive domains. Active inference is a “first principles” approach to understanding behavior and the brain, framed in terms of a single imperative to minimize free energy. The book emphasizes the implications of the free energy principle for understanding how the brain works. It first introduces active inference both conceptually and formally, contextualizing it within current theories of cognition. It then provides specific examples of computational models that use active inference to explain such cognitive phenomena as perception, attention, memory, and planning.

Author : D.L. McLeish,Christopher G. Small
Publisher : Springer Science & Business Media
Page : 131 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461238720

Get Book

The Theory and Applications of Statistical Interference Functions by D.L. McLeish,Christopher G. Small Pdf

This monograph arose out of a desire to develop an approach to statistical infer ence that would be both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important practical problems. In the latter category, the problems of inference for stochastic processes (which arise com monly in engineering and biological applications) come to mind. Classes of estimating functions seem to be promising in this respect. The monograph examines some of the consequences of extending standard concepts of ancillarity, sufficiency and complete ness into this setting. The reader should note that the development is mathematically "mature" in its use of Hilbert space methods but not, we believe, mathematically difficult. This is in keeping with our desire to construct a theory that is rich in statistical tools for infer ence without the difficulties found in modern developments, such as likelihood analysis of stochastic processes or higher order methods, to name but two. The fundamental notions of orthogonality and projection are accessible to a good undergraduate or beginning graduate student. We hope that the monograph will serve the purpose of enriching the methods available to statisticians of various interests.

Author : Alexander Bochman
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 53,6 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9783662045602

Get Book

A Logical Theory of Nonmonotonic Inference and Belief Change by Alexander Bochman Pdf

This is the first book that integrates nonmonotonic reasoning and belief change into a single framework from an artificial intelligence logic point-of-view. The approach to both these subjects is based on a powerful notion of an epistemic state that subsumes both existing models for nonmonotonic inference and current models for belief change. Many results and constructions in the book are completely new and have not appeared earlier in the literature.

Author : Henry Hughes
Publisher : Palala Press
Page : 282 pages
File Size : 43,5 Mb
Release : 2016-05-17
Category : Electronic
ISBN : 1356959857

Get Book

The Theory of Inference by Henry Hughes Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.