Information, Inference and Decision


Book Description

Under the title 'Information, Inference and Decision' this volume in the Theory and Decision Library presents some papers on issues from the borderland of statistical inference philosophy and epistemology, written by statisticians and decision theorists who belonged or are allied to the former Saarbriicken school of statistical decision theory. In the first part I make an attempt to outline an objective theory of inductive behaviour, on the basis of R. A. Fisher's statistical inference philosophy, on the one hand, and R. Carnap's inductive logic, on the other. A special problem arising in the context of the new theory, viz., the problem of vagueness of concepts (in particular in the social sciences) is treated separately by H. Skala and myself. B. Leiner has contributed some biographical and bibliographical notes on the objective theory of inductive behaviour. Part II is concerned with inference philosophy. D. A. S. Fraser, the founder of structural inference theory, characterizes and compares some inference philosophies, and discusses his own and the arguments of the critics of his structural theory. In my opinion, Fraser's structural infer ence theory is suited to complete Fisher's inference philosophy in some essential points, if not to replace it. An interesting task for future re search work is to establish the connection between Fraser's theory and Carnap's ideas in the framework of an objective theory of inductive behaviour.




Information Theory, Inference and Learning Algorithms


Book Description

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.




An Introduction to Bayesian Inference and Decision


Book Description

CD-ROM contains: Beta Distribution Generator (Excel file) ; Binomial Distribution Generator (Excel file) ; book exercises (MS Word files) ; book figures (Powerpoint files) ; TreeAge Data decision trees for some of the examples in the book ; Demonstration versions of TreeAge Data and Lumina Analytica.




On Science, Inference, Information and Decision-Making


Book Description

There are two competing pictures of science. One considers science as a system of inferences, whereas another looks at science as a system of actions. The essays included in this collection offer a view which intends to combine both pictures. This compromise is well illustrated by Szaniawski's analysis of statistical inferences. It is shown that traditional approaches to the foundations of statistics do not need to be regarded as conflicting with each other. Thus, statistical rules can be treated as rules of behaviour as well as rules of inference. Szaniawski's uniform approach relies on the concept of rationality, analyzed from the point of view of decision theory. Applications of formal tools to the problem of justice and division of goods shows that the concept of rationality has a wider significance. Audience: The book will be of interest to philosophers of science, logicians, ethicists and mathematicians.







On Science, Inference, Information and Decision-Making


Book Description

There are two competing pictures of science. One considers science as a system of inferences, whereas another looks at science as a system of actions. The essays included in this collection offer a view which intends to combine both pictures. This compromise is well illustrated by Szaniawski's analysis of statistical inferences. It is shown that traditional approaches to the foundations of statistics do not need to be regarded as conflicting with each other. Thus, statistical rules can be treated as rules of behaviour as well as rules of inference. Szaniawski's uniform approach relies on the concept of rationality, analyzed from the point of view of decision theory. Applications of formal tools to the problem of justice and division of goods shows that the concept of rationality has a wider significance. Audience: The book will be of interest to philosophers of science, logicians, ethicists and mathematicians.




Inference and Decision


Book Description




Inference, Method and Decision


Book Description

This book grew out of previously published papers of mine composed over a period of years; they have been reworked (sometimes beyond recognition) so as to form a reasonably coherent whole. Part One treats of informative inference. I argue (Chapter 2) that the traditional principle of induction in its clearest formulation (that laws are confirmed by their positive cases) is clearly false. Other formulations in terms of the 'uniformity of nature' or the 'resemblance of the future to the past' seem to me hopelessly unclear. From a Bayesian point of view, 'learning from experience' goes by conditionalization (Bayes' rule). The traditional stum bling block for Bayesians has been to fmd objective probability inputs to conditionalize upon. Subjective Bayesians allow any probability inputs that do not violate the usual axioms of probability. Many subjectivists grant that this liberality seems prodigal but own themselves unable to think of additional constraints that might plausibly be imposed. To be sure, if we could agree on the correct probabilistic representation of 'ignorance' (or absence of pertinent data), then all probabilities obtained by applying Bayes' rule to an 'informationless' prior would be objective. But familiar contra dictions, like the Bertrand paradox, are thought to vitiate all attempts to objectify 'ignorance'. BuUding on the earlier work of Sir Harold Jeffreys, E. T. Jaynes, and the more recent work ofG. E. P. Box and G. E. Tiao, I have elected to bite this bullet. In Chapter 3, I develop and defend an objectivist Bayesian approach.




Bayesian Inference


Book Description

This new edition offers a comprehensive introduction to the analysis of data using Bayes rule. It generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. This is particularly useful when the observed parameter is barely above the background or the histogram of multiparametric data contains many empty bins, so that the determination of the validity of a theory cannot be based on the chi-squared-criterion. In addition to the solutions of practical problems, this approach provides an epistemic insight: the logic of quantum mechanics is obtained as the logic of unbiased inference from counting data. New sections feature factorizing parameters, commuting parameters, observables in quantum mechanics, the art of fitting with coherent and with incoherent alternatives and fitting with multinomial distribution. Additional problems and examples help deepen the knowledge. Requiring no knowledge of quantum mechanics, the book is written on introductory level, with many examples and exercises, for advanced undergraduate and graduate students in the physical sciences, planning to, or working in, fields such as medical physics, nuclear physics, quantum mechanics, and chaos.




Foundations of Info-metrics


Book Description

Info-metrics is the science of modeling, reasoning, and drawing inferences under conditions of noisy and insufficient information. It is at the intersection of information theory, statistical inference, and decision-making under uncertainty. It plays an important role in helping make informed decisions even when there is inadequate or incomplete information because it provides a framework to process available information with minimal reliance on assumptions that cannot be validated. In this pioneering book, Amos Golan, a leader in info-metrics, focuses on unifying information processing, modeling and inference within a single constrained optimization framework. Foundations of Info-Metrics provides an overview of modeling and inference, rather than a problem specific model, and progresses from the simple premise that information is often insufficient to provide a unique answer for decisions we wish to make. Each decision, or solution, is derived from the available input information along with a choice of inferential procedure. The book contains numerous multidisciplinary applications and case studies, which demonstrate the simplicity and generality of the framework in real world settings. Examples include initial diagnosis at an emergency room, optimal dose decisions, election forecasting, network and information aggregation, weather pattern analyses, portfolio allocation, strategy inference for interacting entities, incorporation of prior information, option pricing, and modeling an interacting social system. Graphical representations illustrate how results can be visualized while exercises and problem sets facilitate extensions. This book is this designed to be accessible for researchers, graduate students, and practitioners across the disciplines.