Principles of Uncertainty

Author: Joseph B. Kadane
Publisher: CRC Press
ISBN: 1439861617
Format: PDF, ePub, Mobi
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An intuitive and mathematical introduction to subjective probability and Bayesian statistics. An accessible, comprehensive guide to the theory of Bayesian statistics, Principles of Uncertainty presents the subjective Bayesian approach, which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. Both rigorous and friendly, the book contains: Introductory chapters examining each new concept or assumption Just-in-time mathematics – the presentation of ideas just before they are applied Summary and exercises at the end of each chapter Discussion of maximization of expected utility The basics of Markov Chain Monte Carlo computing techniques Problems involving more than one decision-maker Written in an appealing, inviting style, and packed with interesting examples, Principles of Uncertainty introduces the most compelling parts of mathematics, computing, and philosophy as they bear on statistics. Although many books present the computation of a variety of statistics and algorithms while barely skimming the philosophical ramifications of subjective probability, this book takes a different tack. By addressing how to think about uncertainty, this book gives readers the intuition and understanding required to choose a particular method for a particular purpose.

Topics on Methodological and Applied Statistical Inference

Author: Tonio Di Battista
Publisher: Springer
ISBN: 3319440934
Format: PDF
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This book brings together selected peer-reviewed contributions from various research fields in statistics, and highlights the diverse approaches and analyses related to real-life phenomena. Major topics covered in this volume include, but are not limited to, bayesian inference, likelihood approach, pseudo-likelihoods, regression, time series, and data analysis as well as applications in the life and social sciences. The software packages used in the papers are made available by the authors. This book is a result of the 47th Scientific Meeting of the Italian Statistical Society, held at the University of Cagliari, Italy, in 2014.

Introduction to Hierarchical Bayesian Modeling for Ecological Data

Author: Eric Parent
Publisher: CRC Press
ISBN: 1584889209
Format: PDF, ePub, Mobi
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Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts and techniques of the Bayesian paradigm from a practical point of view using real case studies. They emphasize how hierarchical Bayesian modeling supports multidimensional models involving complex interactions between parameters and latent variables. Data sets, exercises, and R and WinBUGS codes are available on the authors’ website. This book shows how Bayesian statistical modeling provides an intuitive way to organize data, test ideas, investigate competing hypotheses, and assess degrees of confidence of predictions. It also illustrates how conditional reasoning can dismantle a complex reality into more understandable pieces. As conditional reasoning is intimately linked with Bayesian thinking, considering hierarchical models within the Bayesian setting offers a unified and coherent framework for modeling, estimation, and prediction.

Pragmatics of Uncertainty

Author: Joseph B. Kadane
Publisher: CRC Press
ISBN: 1498719856
Format: PDF
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A fair question to ask of an advocate of subjective Bayesianism (which the author is) is "how would you model uncertainty?" In this book, the author writes about how he has done it using real problems from the past, and offers additional comments about the context in which he was working.

Handbook of Applied Hydrology Second Edition

Author: Vijay P. Singh
Publisher: McGraw Hill Professional
ISBN: 0071835105
Format: PDF, Kindle
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Fully Updated Hydrology Principles, Methods, and Applications Thoroughly revised for the first time in 50 years, this industry-standard resource features chapter contributions from a “who’s who” of international hydrology experts. Compiled by a colleague of the late Dr. Chow, Chow’s Handbook of Applied Hydrology, Second Edition, covers scientific and engineering fundamentals and presents all-new methods, processes, and technologies. Complete details are provided for the full range of ecosystems and models. Advanced chapters look to the future of hydrology, including climate change impacts, extraterrestrial water, social hydrology, and water security. Chow’s Handbook of Applied Hydrology, Second Edition, covers: · The Fundamentals of Hydrology · Data Collection and Processing · Hydrology Methods · Hydrologic Processes and Modeling · Sediment and Pollutant Transport · Hydrometeorologic and Hydrologic Extremes · Systems Hydrology · Hydrology of Large River and Lake Basins · Applications and Design · The Future of Hydrology

A Primer on Linear Models

Author: John F. Monahan
Publisher: CRC Press
ISBN: 9781420062045
Format: PDF
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A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods. With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss–Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers. This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.

Spatio Temporal Methods in Environmental Epidemiology

Author: Gavin Shaddick
Publisher: CRC Press
ISBN: 1482237040
Format: PDF, Docs
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Teaches Students How to Perform Spatio-Temporal Analyses within Epidemiological Studies Spatio-Temporal Methods in Environmental Epidemiology is the first book of its kind to specifically address the interface between environmental epidemiology and spatio-temporal modeling. In response to the growing need for collaboration between statisticians and environmental epidemiologists, the book links recent developments in spatio-temporal methodology with epidemiological applications. Drawing on real-life problems, it provides the necessary tools to exploit advances in methodology when assessing the health risks associated with environmental hazards. The book’s clear guidelines enable the implementation of the methodology and estimation of risks in practice. Designed for graduate students in both epidemiology and statistics, the text covers a wide range of topics, from an introduction to epidemiological principles and the foundations of spatio-temporal modeling to new research directions. It describes traditional and Bayesian approaches and presents the theory of spatial, temporal, and spatio-temporal modeling in the context of its application to environmental epidemiology. The text includes practical examples together with embedded R code, details of specific R packages, and the use of other software, such as WinBUGS/OpenBUGS and integrated nested Laplace approximations (INLA). A supplementary website provides additional code, data, examples, exercises, lab projects, and more. Representing a major new direction in environmental epidemiology, this book—in full color throughout—underscores the increasing need to consider dependencies in both space and time when modeling epidemiological data. Students will learn how to identify and model patterns in spatio-temporal data as well as exploit dependencies over space and time to reduce bias and inefficiency.