Download or read book Some Methods of Approximating Distribution Functions with Application to Some Inference Problems written by Osebekwin Ebenezer Asiribo and published by . This book was released on 1986 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Causal Inference written by Judea Pearl and published by Createspace Independent Publishing Platform. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper summarizes recent advances in causal inference and underscores the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called "causal effects" or "policy evaluation") (2) queries about probabilities of counterfactuals, (including assessment of "regret," "attribution" or "causes of effects") and (3) queries about direct and indirect effects (also known as "mediation"). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both. The tools are demonstrated in the analyses of mediation, causes of effects, and probabilities of causation. -- p. 1.
Download or read book On the Theory and Methods of Statistical Inference written by Gerald L. Smith and published by . This book was released on 1967 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical inference is the process of intelligently using information from observations and experiments to draw conclusions and make decisions. The class of inference problems includes all the classical statistical problems of point and parameter estimation, regression analysis, and hypothesis testing, as well as the engineering problems of control and filtering. In order that inference problems may be stated in mathematical terms, it is necessary to utilize mathematical of the often intangible entities called knowledge and goodness (or optimality). Probability is the measure utilized for knowledge, and loss functions serve as measures of optimality. The conversion of knowledge and goodness into functional or numerical terms is usually quite subjective and thus to a substantial extent arbitrary. Nevertheless, the conversion is necessary if the language of mathematics is to be employed in the inference logic. The various mathematical methods developed, under different assumptions, for solving inferential problems are unavoidable related since all are (in principle) reducible to a common form. Some of the most fundamental of these -- least squares, minimum variance, and maximum likelihood -- are reviewed to show their interrelationships. The newer developments of sequential analysis and filtering are similarly described. All of these are shown to be special cases of the general theory of Bayesian decision making. The Bayesian decision theory requires the specification of an appropriate loss function. The optimum decision is then defined as that which minimizes the mathematical expectation of this loss. Computation of this expectation requires obtaining the posterior distribution of the unknown state based on prescribed scientific observations. Under restrictive conditions the computations involved in this general decision-making procedure are reducible to relatively simple forms. For application under more general conditions methods of approximation and efficient computational algorithms are presently being developed.
Download or read book Some Methods of Approximation Distribution Functions written by Rudy Alan Gideon and published by . This book was released on 1970 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Machine learning using approximate inference written by Christian Andersson Naesseth and published by Linköping University Electronic Press. This book was released on 2018-11-27 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic decision making and pattern recognition under uncertainty are difficult tasks that are ubiquitous in our everyday life. The systems we design, and technology we develop, requires us to coherently represent and work with uncertainty in data. Probabilistic models and probabilistic inference gives us a powerful framework for solving this problem. Using this framework, while enticing, results in difficult-to-compute integrals and probabilities when conditioning on the observed data. This means we have a need for approximate inference, methods that solves the problem approximately using a systematic approach. In this thesis we develop new methods for efficient approximate inference in probabilistic models. There are generally two approaches to approximate inference, variational methods and Monte Carlo methods. In Monte Carlo methods we use a large number of random samples to approximate the integral of interest. With variational methods, on the other hand, we turn the integration problem into that of an optimization problem. We develop algorithms of both types and bridge the gap between them. First, we present a self-contained tutorial to the popular sequential Monte Carlo (SMC) class of methods. Next, we propose new algorithms and applications based on SMC for approximate inference in probabilistic graphical models. We derive nested sequential Monte Carlo, a new algorithm particularly well suited for inference in a large class of high-dimensional probabilistic models. Then, inspired by similar ideas we derive interacting particle Markov chain Monte Carlo to make use of parallelization to speed up approximate inference for universal probabilistic programming languages. After that, we show how we can make use of the rejection sampling process when generating gamma distributed random variables to speed up variational inference. Finally, we bridge the gap between SMC and variational methods by developing variational sequential Monte Carlo, a new flexible family of variational approximations.
Download or read book Some Problems in Statistical Inference written by J. J. Gart and published by . This book was released on 1958 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimation of Dependences Based on Empirical Data written by V. Vapnik and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twenty-?ve years have passed since the publication of the Russian version of the book Estimation of Dependencies Based on Empirical Data (EDBED for short). Twen- ?ve years is a long period of time. During these years many things have happened. Looking back, one can see how rapidly life and technology have changed, and how slow and dif?cult it is to change the theoretical foundation of the technology and its philosophy. I pursued two goals writing this Afterword: to update the technical results presented in EDBED (the easy goal) and to describe a general picture of how the new ideas developed over these years (a much more dif?cult goal). The picture which I would like to present is a very personal (and therefore very biased) account of the development of one particular branch of science, Empirical - ference Science. Such accounts usually are not included in the content of technical publications. I have followed this rule in all of my previous books. But this time I would like to violate it for the following reasons. First of all, for me EDBED is the important milestone in the development of empirical inference theory and I would like to explain why. S- ond, during these years, there were a lot of discussions between supporters of the new 1 paradigm (now it is called the VC theory ) and the old one (classical statistics).
Download or read book Aspects of Statistical Inference written by A. H. Welsh and published by John Wiley & Sons. This book was released on 1996-10-10 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relevant, concrete, and thorough--the essential data-based text onstatistical inference The ability to formulate abstract concepts and draw conclusionsfrom data is fundamental to mastering statistics. Aspects ofStatistical Inference equips advanced undergraduate and graduatestudents with a comprehensive grounding in statistical inference,including nonstandard topics such as robustness, randomization, andfinite population inference. A. H. Welsh goes beyond the standard texts and expertly synthesizesbroad, critical theory with concrete data and relevant topics. Thetext follows a historical framework, uses real-data sets andstatistical graphics, and treats multiparameter problems, yet isultimately about the concepts themselves. Written with clarity and depth, Aspects of Statistical Inference: * Provides a theoretical and historical grounding in statisticalinference that considers Bayesian, fiducial, likelihood, andfrequentist approaches * Illustrates methods with real-data sets on diabetic retinopathy,the pharmacological effects of caffeine, stellar velocity, andindustrial experiments * Considers multiparameter problems * Develops large sample approximations and shows how to use them * Presents the philosophy and application of robustness theory * Highlights the central role of randomization in statistics * Uses simple proofs to illuminate foundational concepts * Contains an appendix of useful facts concerning expansions,matrices, integrals, and distribution theory Here is the ultimate data-based text for comparing and presentingthe latest approaches to statistical inference.
Download or read book Distribution Free Statistical Methods written by J. S. Maritz and published by Springer. This book was released on 1981 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic concepts in distribution-free methods; One-sample location problems; Miscellaneous one-sample problems; Two-sample problems; Straight-line regression; Multiple regression and general linear models; Bivariate problems; Appendix; Bibliography.
Download or read book Bulletin Institute of Mathematical Statistics written by Institute of Mathematical Statistics and published by . This book was released on 1991 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multidisciplinary Research in Control written by Laura Giarré and published by Springer. This book was released on 2003-09-04 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mohammed Dahleh symposium brought together leading researchers in several areas of engineering and science. Many of the presentations focused on new emerging research areas of key significance. These new areas have in common that the dynamics and control theory and methods provide the appropriate framework for the understanding of the corresponding phenomena, while at the same time providing many of the tools necessary for their application to relevant technologies. Examples of these opportunities include the areas of systems biology, quantum feedback and control, fluid dynamics, and control applications in nanotechnology. This collected volume demonstrates the importance of these emerging areas in the current research agenda in science and technology and shows that a unique opportunity exists to drastically extend the scope and impact of dynamics and control methods far beyond their traditional areas of application in engineering.
Download or read book An Author and Permuted Title Index to Selected Statistical Journals written by Brian L. Joiner and published by . This book was released on 1970 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
Download or read book Exponential Distribution written by K. Balakrishnan and published by Routledge. This book was released on 2019-01-22 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2004 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inference and Asymptotics written by D.R. Cox and published by Routledge. This book was released on 2017-10-19 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the original theme and gives a systematic account of some recent developments in asymptotic parametric inference from a likelihood-based perspective. Chapters 1-4 are relatively elementary and provide first a review of key concepts such as likelihood, sufficiency, conditionality, ancillarity, exponential families and transformation models. Then first-order asymptotic theory is set out, followed by a discussion of the need for higher-order theory. This is then developed in some generality in Chapters 5-8. A final chapter deals briefly with some more specialized issues. The discussion emphasizes concepts and techniques rather than precise mathematical verifications with full attention to regularity conditions and, especially in the less technical chapters, draws quite heavily on illustrative examples. Each chapter ends with outline further results and exercises and with bibliographic notes. Many parts of the field discussed in this book are undergoing rapid further development, and in those parts the book therefore in some respects has more the flavour of a progress report than an exposition of a largely completed theory.
