Download or read book The Estimation Of Probabilities written by Irving John Good and published by MIT Press. This book was released on 2003-03-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of how to estimate probabilities has interested philosophers, statisticians, actuaries, and mathematicians for a long time. It is currently of interest for automatic recognition, medical diagnosis, and artificial intelligence in general. This monograph reviews existing methods, including those that are new or have not been written up in a connected manner. The problem of how to estimate probabilities has interested philosophers, statisticians, actuaries, and mathematicians for a long time. It is currently of interest for automatic recognition, medical diagnosis, and artificial intelligence in general. The main purpose of this monograph is to review existing methods, especially those that are new or have not been written about in an organized way. The need for nontrivial theory arises because our samples are usually too small for us to rely exclusively on the frequency definition of probability. Most of the techniques described in this book depend on a modern Bayesian approach. The maximum-entropy principle, also relevant to this discussion, is used in the last chapter. It is hoped that the book will stimulate further work in a field whose importance will increasingly be recognized. Methods for estimating probabilities are related to another part of statistics, namely, significance testing, and example of this relationship are also presented. Many readers will be persuaded by this work that it is necessary to make use of a theory of subjective probability in order to estimate physical probabilities and also that a useful idea is that of a hierarchy of three types of probability which can sometimes be identified with physical, logical, and subjective probabilities.
Download or read book Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems written by Jerome Morio and published by Woodhead Publishing. This book was released on 2015-11-16 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rare event probability (10-4 and less) estimation has become a large area of research in the reliability engineering and system safety domains. A significant number of methods have been proposed to reduce the computation burden for the estimation of rare events from advanced sampling approaches to extreme value theory. However, it is often difficult in practice to determine which algorithm is the most adapted to a given problem.Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach provides a broad up-to-date view of the current available techniques to estimate rare event probabilities described with a unified notation, a mathematical pseudocode to ease their potential implementation and finally a large spectrum of simulation results on academic and realistic use cases. Provides a broad overview of the practical approach of rare event methods. Includes algorithms that are applied to aerospace benchmark test cases Offers insight into practical tuning issues
Download or read book Estimating and Choosing written by Georges Matheron and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the beginning of modern probability theory in the seventeenth century there has been a continuous debate over the meaning and applicability of the concept of probability. This book presents a coherent and well thoughtout framework for the use of probabilistic models to describe unique phenomena in a purely objective way. Although Estimating and Choosing was written with geostatistical applications in mind, the approach is of general applicability across the whole spectrum of probabilistic modelling. The only full-fledged treatment of the foundations of practical probability modelling ever written, this book fills an important gap in the literature of probability and statistics.
Download or read book Sequential Estimation written by Malay Ghosh and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only comprehensive guide to the theory and practice of one oftoday's most important probabilistic techniques The past 15 years have witnessed many significant advances insequential estimation, especially in the areas of three-stage andnonparametric methodology. Yet, until now, there were no referencesdevoted exclusively to this rapidly growing statisticalfield. Sequential Estimation is the first, single-source guide to thetheory and practice of both classical and modern sequentialestimation techniques--including parametric and nonparametricmethods. Researchers in sequential analysis will appreciate theunified, logically integrated treatment of the subject, as well ascoverage of important contemporary procedures not covered in moregeneral sequential analysis texts, such as: * Shrinkage estimation * Empirical and hierarchical Bayes procedures * Multistage sampling and accelerated sampling procedures * Time-sequential estimation * Sequential estimation in finite population sampling * Reliability estimation and capture-recapture methodologiesleading to sequential tagging schemes An indispensable resource for researchers in sequential analysis,Sequential Estimation is an ideal graduate-level text as well.
Download or read book Probability Random Variables Statistics and Random Processes written by Ali Grami and published by John Wiley & Sons. This book was released on 2019-04-02 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this book is on the basic principles and practical applications of the fundamental concepts that are extensively used in various Engineering disciplines as well as in a variety of programs in Life and Social Sciences. The text provides students with the requisite building blocks of knowledge they require to understand and progress in their areas of interest. With a simple, clear-cut style of writing, the intuitive explanations, insightful examples, and practical applications are the hallmarks of this book. The text consists of twelve chapters divided into four parts. Part-I, Probability (Chapters 1 – 3), lays a solid groundwork for probability theory, and introduces applications in counting, gambling, reliability, and security. Part-II, Random Variables (Chapters 4 – 7), discusses in detail multiple random variables, along with a multitude of frequently-encountered probability distributions. Part-III, Statistics (Chapters 8 – 10), highlights estimation and hypothesis testing. Part-IV, Random Processes (Chapters 11 – 12), delves into the characterization and processing of random processes. Other notable features include: Most of the text assumes no knowledge of subject matter past first year calculus and linear algebra With its independent chapter structure and rich choice of topics, a variety of syllabi for different courses at the junior, senior, and graduate levels can be supported A supplemental website includes solutions to about 250 practice problems, lecture slides, and figures and tables from the text Given its engaging tone, grounded approach, methodically-paced flow, thorough coverage, and flexible structure, Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications clearly serves as a must textbook for courses not only in Electrical Engineering, but also in Computer Engineering, Software Engineering, and Computer Science.
Download or read book The Estimation of Probability Densities written by Richard Aaron Kronmal and published by . This book was released on 1964 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Neural Networks for Conditional Probability Estimation written by Dirk Husmeier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conventional applications of neural networks usually predict a single value as a function of given inputs. In forecasting, for example, a standard objective is to predict the future value of some entity of interest on the basis of a time series of past measurements or observations. Typical training schemes aim to minimise the sum of squared deviations between predicted and actual values (the 'targets'), by which, ideally, the network learns the conditional mean of the target given the input. If the underlying conditional distribution is Gaus sian or at least unimodal, this may be a satisfactory approach. However, for a multimodal distribution, the conditional mean does not capture the relevant features of the system, and the prediction performance will, in general, be very poor. This calls for a more powerful and sophisticated model, which can learn the whole conditional probability distribution. Chapter 1 demonstrates that even for a deterministic system and 'be nign' Gaussian observational noise, the conditional distribution of a future observation, conditional on a set of past observations, can become strongly skewed and multimodal. In Chapter 2, a general neural network structure for modelling conditional probability densities is derived, and it is shown that a universal approximator for this extended task requires at least two hidden layers. A training scheme is developed from a maximum likelihood approach in Chapter 3, and the performance ofthis method is demonstrated on three stochastic time series in chapters 4 and 5.
Download or read book A Mathematical Primer for Social Statistics written by John Fox and published by SAGE Publications. This book was released on 2021-01-11 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Primer for Social Statistics, Second Edition presents mathematics central to learning and understanding statistical methods beyond the introductory level: the basic "language" of matrices and linear algebra and its visual representation, vector geometry; differential and integral calculus; probability theory; common probability distributions; statistical estimation and inference, including likelihood-based and Bayesian methods. The volume concludes by applying mathematical concepts and operations to a familiar case, linear least-squares regression. The Second Edition pays more attention to visualization, including the elliptical geometry of quadratic forms and its application to statistics. It also covers some new topics, such as an introduction to Markov-Chain Monte Carlo methods, which are important in modern Bayesian statistics. A companion website includes materials that enable readers to use the R statistical computing environment to reproduce and explore computations and visualizations presented in the text. The book is an excellent companion to a "math camp" or a course designed to provide foundational mathematics needed to understand relatively advanced statistical methods.
Download or read book Probability Random Processes and Estimation Theory for Engineers written by Henry Stark and published by Prentice Hall. This book was released on 1986 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of probability and random processes.
Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Download or read book Probability Theory written by and published by Allied Publishers. This book was released on 2013 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory
Download or read book Estimation of Probabilities in Problems of Selection written by John Weldon Boddie and published by . This book was released on 1974 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book All of Statistics written by Larry Wasserman and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
Download or read book A Modern Approach to Probability Theory written by Bert E. Fristedt and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
Download or read book Understanding and Calculating the Odds written by Catalin Barboianu and published by INFAROM Publishing. This book was released on 2006 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents not only the mathematical concept of probability, but also its philosophical aspects, the relativity of probability and its applications and even the psychology of probability. All explanations are made in a comprehensible manner and are supported with suggestive examples from nature and daily life, and even with challenging math paradoxes. (Mathematics)
Download or read book Probability and Bayesian Modeling written by Jim Albert and published by CRC Press. This book was released on 2019-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
Download or read book Foundations of Estimation Theory written by L. Kubacek and published by Elsevier. This book was released on 2012-12-02 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of estimation theory renders the processing of experimental results both rational and effective, and thus helps not only to make our knowledge more precise but to determine the measure of its reliability. As a consequence, estimation theory is indispensable in the analysis of the measuring processes and of experiments in general.The knowledge necessary for studying this book encompasses the disciplines of probability and mathematical statistics as studied in the third or fourth year at university. For readers interested in applications, comparatively detailed chapters on linear and quadratic estimations, and normality of observation vectors have been included. Chapter 2 includes selected items of information from algebra, functional analysis and the theory of probability, intended to facilitate the reading of the text proper and to save the reader looking up individual theorems in various textbooks and papers; it is mainly devoted to the reproducing kernel Hilbert spaces, helpful in solving many estimation problems. The text proper of the book begins with Chapter 3. This is divided into two parts: the first deals with sufficient statistics, complete sufficient statistics, minimal sufficient statistics and relations between them; the second contains the mostimportant inequalities of estimation theory for scalar and vector valued parameters and presents properties of the exponential family of distributions.The fourth chapter is an introduction to asymptotic methods of estimation. The method of statistical moments and the maximum-likelihood method are investigated. The sufficient conditions for asymptotical normality of the estimators are given for both methods. The linear and quadratic methods of estimation are dealt with in the fifth chapter. The method of least squares estimation is treated. Five basic regular versions of the regression model and the unified linear model of estimation are described. Unbiased estimators for unit dispersion (factor of the covariance matrix) are given for all mentioned cases. The equivalence of the least-squares method to the method of generalized minimum norm inversion of the design matrix of the regression model is studied in detail. The problem of estimating the covariance components in the mixed model is mentioned as well. Statistical properties of linear and quadratic estimators developed in the fifth chapter in the case of normally distributed errors of measurement are given in Chapter 6. Further, the application of tensor products of Hilbert spaces generated by the covariance matrix of random error vector of observations is demonstrated. Chapter 7 reviews some further important methods of estimation theory. In the first part Wald's method of decision functions is applied to the construction of estimators. The method of contracted estimators and the method of Hoerl and Kennard are presented in the second part. The basic ideas of robustness and Bahadur's approach to estimation theory are presented in the third and fourth parts of this last chapter.
