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Probability & Statistics - Bayesian Analysis

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Chain Event Graphs: Chapman & Hall/CRC Computer Science and Data Analysis Series
by Collazo, Rodrigo A.    Goergen, Christiane    Smith, Jim Q.
(Hardcover - English - 9781498729604)
Written by some major contributors to the development of this class of graphical models, Chain Event Graphs introduces a viable and straightforward new tool for statistical inference, model selection and learning techniques. The book extends established technologies used in the study of discrete Bayesian Networks so that they apply in a much more general setting br As the first book on Chain Event Graphs, this monograph is expected to become a landmark work on the use of event trees and coloured probability trees in statistics, and to lead to the increased use of such tree models to describe hypotheses about how events might unfold. Features: ul li int ..
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Statistical formulas: for professional studies
by Nyberg, Svein Olav       
(Paperback - English - 9781546718857)
This book of statistical formulas is primarily intended for statistics for professional studies. The typical user will see only a single statistics course, or maybe two if he decides to go advanced, for his entire life. This is not to say that a beginning student of statistics or mathematics may not also find it useful at the start of their studies, but they should not expect it to be their faithful companion far into the more advanced courses. The main angle for statistical inference in this book of formulas is bayesian, simply because it is the simplest and most logical route to applying probability to the many uncertainties in life, and not the least to profe ..
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Weakly Stationary Random Fields, Invariant Subspaces and Applications
by Mandrekar, Vidyadhar S.    Redett, David A.   
(Hardcover - English - 9781138562240)
The first book to examine weakly stationary random fields and their connections with invariant subspaces (an area associated with functional analysis). It reviews current literature, presents central issues and most important results within the area. For advanced Ph.D. students, researchers, especially those conducting research on Gaussian theory. ..
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Model Choice and Model Aggregation
by Saporta, Gilbert    Bertrand, Frédéric    Droesbeke, Jean-Jacques
(Paperback - English - 9782710811770)
For over forty years, choosing a statistical model thanks to data consisted in optimizing a criterion based on penalized likelihood (H. Akaike, 1973) or penalized least squares (C. Mallows, 1973). These methods are valid for predictive model choice (regression, classification) and for descriptive models (clustering, mixtures). Most of their properties are asymptotic, but a non-asymptotic theory has emerged at the end of the last century (Birg -Massart, 1997). Instead of choosing the best model among several candidates, model aggregation combines different models, often linearly, allowing better predictions. Bayesian statistics provide a useful framework for mode ..
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Measure and Probability
by Athreya, Siva    Sunder, V. S.   
(Paperback - English - 9781138114180)
This book covers the fundamentals of measure theory and probability theory. It begins with the construction of Lebesgue measure via Caratheodory's outer measure approach and goes on to discuss integration and standard convergence theorems and contains an entire chapter devoted to complex measures, Lp spaces, Radon-Nikodym theorem, and the Riesz representation theorem. It presents the elements of probability theory, the law of large numbers, and central limit theorem. The book then discusses discrete time Markov chains, stationary distributions and limit theorems. The appendix covers many basic topics such as metric spaces, topological spaces and the Stone-Weiers ..
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The Theory of Stochastic Processes
by Cox, D. R.       
(Hardcover - English - 9781138460348)
This book should be of interest to undergraduate and postgraduate students of probability theory. ..
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How to Win More: Strategies for Increasing a Lottery Win
by Henze, Norbert    Riedwyl, Hans   
(Hardcover - English - 9781138469686)
This book is designed to provide valuable insight into how to improve the return on your investment when playing the lottery. While it does not promise that you will win more often, it does show you how to improve the odds of winning larger amounts when your numbers do come up. So, when you do win that million-dollar jackpot, you will be less likely to have to share it with anyone else. br Among the intriguing topics covered are the most popular (and the most foolish) combinations of numbers, why it is impossible to improve the odds of any legitimate lottery, how popular (and thus unprofitable) an attractive-looking ticket might be, why not to follow the sugges ..
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Elements of Simulation
by Morgan, Byron J. T.       
(Hardcover - English - 9781138469716)
This book provides a guide to the elements of simulation in statistics, which will include developments and which may be used either as a teaching text or as a source of reference. It is widely used for teaching statistics in schools. ..
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Large Covariance and Autocovariance Matrices
by Bose, Arup    Bhattacharjee, Monika   
(Hardcover - English - 9781138303867)
Large Covariance and Autocovariance Matrices brings together a collection of recent results on sample covariance and autocovariance matrices in high-dimensional models and novel ideas on how to use them for statistical inference in one or more high-dimensional time series models. The prerequisites include knowledge of elementary multivariate analysis, basic time series analysis and basic results in stochastic convergence. Partis on different methods of estimation of large covariance matrices and auto-covariance matrices and properties of these estimators. Part II covers the relevant material on random matrix theory and non-commutative probability. Part III prov ..
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Nonlinear Time Series Analysis
by Tsay, Ruey S.    Chen, Rong   
(Hardcover - English - 9781119264057)
A comprehensive resource that draws a balance between theory and applications of nonlinear time series analysis Nonlinear Time Series Analysis offers an important guide to both parametric and nonparametric methods, nonlinear state-space models, and Bayesian as well as classical approaches to nonlinear time series analysis. The authors--noted experts in the field--explore the advantages and limitations of the nonlinear models and methods and review the improvements upon linear time series models. The need for this book is based on the recent developments in nonlinear time series analysis, statistical learning, dynamic systems and advanced computational method ..
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Random Circulant Matrices
by Bose, Arup    Saha, Koushik   
(Hardcover - English - 9781138351097)
Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k -circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and ..
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Queues
by Cox, D. R.    Cox, D. R.    Smith, Walter
(Hardcover - English - 9781138460317)
This is a classic book on Queues. First published in 1961 it is clearly and concisely introduces the theory of queueing systems and is still just as relevant today. The monograph is aimed at both students and operational research workers concerned with the practical investigations of queueing, although almost every statistician will find its contents of interest. ..
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The Bayesian Way: Introductory Statistics for Economists and Engineers
by Nyberg, Svein Olav       
(Hardcover - English - 9781119246879)
A comprehensive resource that offers an introduction to statistics with a Bayesian angle, for students of professional disciplines like engineering and economics The Bayesian Way offers a basic introduction to statistics that emphasizes the Bayesian approach and is designed for use by those studying professional disciplines like engineering and economics. In addition to the Bayesian approach, the author includes the most common techniques of the frequentist approach. Throughout the text, the author covers statistics from a basic to a professional working level along with a practical understanding of the matter at hand. Filled with helpful illustrations, this ..
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Bayesian Inference: Data Evaluation and Decisions
by Harney, Hanns Ludwig       
(Paperback - English - 9783319824031)
Knowledge an Logic.- Bayes' Theorem.- Probable and Improbable Data.- Descriptions of Distributions I: Real x.- Description of Distributions II: Natural x .- Form Invariance I.- Examples of Invariant Measures.- A Linear Representation of Form Invariance.- Going Beyond Form Invariance: The Geometric Prior.- Inferring the Mean or Standard Deviation.- Form Invariance II: Natural x .- Item Response Theory.- On the Art of Fitting .- Problems and Solutions.- Description of Distributions I.- Real x.- Form Invariance I.- Beyond Form Invariance: The Geometric Prior.- Inferring Mean or Standard Deviation.- Form Invariance II: Natural x .- Item Response Theory.- On the Art ..
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Mathematical Statistics with Applications
by Kapadia, Asha Seth    Chan, Wenyaw    Moyé, Lemuel A.
(Hardcover - English - 9780824754006)
Mathematical statistics typically represents one of the most difficult challenges in statistics, particularly for those with more applied, rather than mathematical, interests and backgrounds. Most textbooks on the subject provide little or no review of the advanced calculus topics upon which much of mathematical statistics relies and furthermore contain material that is wholly theoretical, thus presenting even greater challenges to those interested in applying advanced statistics to a specific area. Mathematical Statistics with Applications presents the background concepts and builds the technical sophistication needed to move on to more advanced studies in mul ..
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Chain Event Graphs: Chapman & Hall/CRC Computer Science and Data Analysis Series
by Collazo, Rodrigo A.    Goergen, Christiane    Smith, Jim Q.
(Paperback - English - 9780367572310)
Written by some major contributors to the development of this class of graphical models, Chain Event Graphs introduces a viable and straightforward new tool for statistical inference, model selection and learning techniques. The book extends established technologies used in the study of discrete Bayesian Networks so that they apply in a much more general setting br As the first book on Chain Event Graphs, this monograph is expected to become a landmark work on the use of event trees and coloured probability trees in statistics, and to lead to the increased use of such tree models to describe hypotheses about how events might unfold. Features: ul li i ..
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Bayesian Inference for Stochastic Processes
by Broemeling, Lyle D.       
(Paperback - English - 9780367572433)
This is the first book designed to introduce Bayesian inference procedures for stochastic processes. There are clear advantages to the Bayesian approach (including the optimal use of prior information). Initially, the book begins with a brief review of Bayesian inference and uses many examples relevant to the analysis of stochastic processes, including the four major types, namely those with discrete time and discrete state space and continuous time and continuous state space. The elements necessary to understanding stochastic processes are then introduced, followed by chapters devoted to the Bayesian analysis of such processes. It is important that a chapter d ..
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Weakly Stationary Random Fields, Invariant Subspaces and Applications
by Mandrekar, Vidyadhar S.    Redett, David A.   
(Paperback - English - 9780367572723)
The first book to examine weakly stationary random fields and their connections with invariant subspaces (an area associated with functional analysis). It reviews current literature, presents central issues and most important results within the area. For advanced Ph.D. students, researchers, especially those conducting research on Gaussian theory. ..
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What Makes Variables Random: Probability for the Applied Researcher
by Veazie, Peter J.       
(Paperback - English - 9780367573713)
strong What Makes Variables Random: Probability for the Applied Researcher strong provides an introduction to the foundations of probability that underlie the statistical analyses used in applied research. By explaining probability in terms of measure theory, it gives the applied researchers a conceptual framework to guide statistical modeling and analysis, and to better understand and interpret results. The book provides a conceptual understanding of probability and its structure. It is intended to augment existing calculus-based textbooks on probability and statistics and is specifically targeted to researchers and advanced undergraduate and graduate stu ..
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Bayesian Methods for Measures of Agreement
by Broemeling, Lyle D.       
(Paperback - English - 9780367577384)
Using WinBUGS to implement Bayesian inferences of estimation and testing hypotheses, strong Bayesian Methods for Measures of Agreement strong presents useful methods for the design and analysis of agreement studies. It focuses on agreement among the various players in the diagnostic process. The author employs a Bayesian approach to provide statistical inferences based on various models of intra- and interrater agreement. He presents many examples that illustrate the Bayesian mode of reasoning and explains elements of a Bayesian application, including prior information, experimental information, the likelihood function, posterior distribution, and predictiv ..
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