*A Tutorial Introduction to Bayesian Analysis*

Author: James V Stone

Publisher: N.A

ISBN: 9780993367946

Category: Mathematics

Page: 186

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## Bayes' Rule With R

Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, a range of accessible examples is used to show how Bayes' rule is actually a natural consequence of common sense reasoning. Bayes' rule is then derived using intuitive graphical representations of probability, and Bayesian analysis is applied to parameter estimation. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to become familiar with the basic principles of Bayesian analysis. Note that this book includes R (3.2) code snippets, which reproduce key numerical results and diagrams.
## Bayes' Rule

In this richly illustrated book, a range of accessible examples are used to show how Bayes' rule is actually a natural consequence of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for the novice who wishes to become familiar with the basic principles of Bayesian analysis.
## Statistik: Klassisch oder Bayes

Die schließende Statistik ist die Wissenschaft davon, aus einer Stichprobe auf die Gesamtheit zu schließen. In ihr gibt es zwei vorherrschende Lehren: die klassische Statistik und die Bayes-Statistik. Die klassische Statistik verwendet zum Schätzen von Parametern und zum Testen von Hypothesen nur die Stichprobe; die bayessche stellt zusätzlich in Rechnung, was man sonst noch über das Problem weiß oder annimmt. Das hängt mit unterschiedlichen Meinungen darüber zusammen, was Wahrscheinlichkeit bedeutet: relative Häufigkeit in Zufallsexperimenten (die klassische Sicht) oder einen Ausdruck des Wissens (die bayessche). Dieses Buch soll die Standpunkte klären und prüfen: Ausgehend vom jeweiligen Wahrscheinlichkeitsbegriff werden klassische und bayessche Methoden entwickelt und auf Schätz- und Testprobleme angewandt, wobei Gemeinsamkeiten und Unterschiede hervorgehoben werden und besonderes Augenmerk auf die Interpretation der Ergebnisse gerichtet ist.
## Doing Bayesian Data Analysis

Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Second Edition provides an accessible approach for conducting Bayesian data analysis, as material is explained clearly with concrete examples. Included are step-by-step instructions on how to carry out Bayesian data analyses in the popular and free software R and WinBugs, as well as new programs in JAGS and Stan. The new programs are designed to be much easier to use than the scripts in the first edition. In particular, there are now compact high-level scripts that make it easy to run the programs on your own data sets. The book is divided into three parts and begins with the basics: models, probability, Bayes’ rule, and the R programming language. The discussion then moves to the fundamentals applied to inferring a binomial probability, before concluding with chapters on the generalized linear model. Topics include metric-predicted variable on one or two groups; metric-predicted variable with one metric predictor; metric-predicted variable with multiple metric predictors; metric-predicted variable with one nominal predictor; and metric-predicted variable with multiple nominal predictors. The exercises found in the text have explicit purposes and guidelines for accomplishment. This book is intended for first-year graduate students or advanced undergraduates in statistics, data analysis, psychology, cognitive science, social sciences, clinical sciences, and consumer sciences in business. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and JAGS software Comprehensive coverage of all scenarios addressed by non-Bayesian textbooks: t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis) Coverage of experiment planning R and JAGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment Provides step-by-step instructions on how to conduct Bayesian data analyses in the popular and free software R and WinBugs
## Wahrscheinlichkeitsrechnung fÃ1⁄4r Dummies

Die Wahrscheinlichkeitsrechnung wird in der Schule oft nur beilï¿1⁄2ufig behandelt, dabei handelt es sich um ein besonders spannendes und alltagstaugliches Teilgebiet der Mathematik. Fï¿1⁄2r alle, die ï¿1⁄2ber dieses Thema noch etwas mehr erfahren wollen oder mï¿1⁄2ssen, erklï¿1⁄2rt Deborah Rumsey verstï¿1⁄2ndlich und mit Humor, was sie unbedingt wissen sollten. Egal ob Kontingenztabelle, zentraler Grenzwertsatz, Stichproben-, Binomial- oder Poissonverteilung, in diesem Buch lernen Sie, was es ist und wie Sie es anwenden. Zu jedem Kapitel finden Sie online eine ï¿1⁄2bungsaufgabe samt Lï¿1⁄2sung, um das Gelernte zu festigen. Auch Tipps zu praktischen Anwendungen - ob bei der Arbeit oder am Pokertisch - kommen nicht zu kurz. So finden Sie in diesem Buch alles, was Sie ï¿1⁄2ber Wahrscheinlichkeitsrechnung unbedingt wissen sollten.
## Option Pricing and Estimation of Financial Models with R

Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
## Statistical Decision Theory and Bayesian Analysis

In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.
## Mathematical Statistics

Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in mathematics.
## Decision Theory

Decision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice. The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives. This book: Provides a rich collection of techniques and procedures. Discusses the foundational aspects and modern day practice. Links foundations to practical applications in biostatistics, computer science, engineering and economics. Presents different perspectives and controversies to encourage readers to form their own opinion of decision making and statistics. Decision Theory is fundamental to all scientific disciplines, including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book.
## A First Course in Bayesian Statistical Methods

A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. Numerous examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.
## A Generative Theory of Relevance

A modern information retrieval system must have the capability to find, organize and present very different manifestations of information – such as text, pictures, videos or database records – any of which may be of relevance to the user. However, the concept of relevance, while seemingly intuitive, is actually hard to define, and it's even harder to model in a formal way. Lavrenko does not attempt to bring forth a new definition of relevance, nor provide arguments as to why any particular definition might be theoretically superior or more complete. Instead, he takes a widely accepted, albeit somewhat conservative definition, makes several assumptions, and from them develops a new probabilistic model that explicitly captures that notion of relevance. With this book, he makes two major contributions to the field of information retrieval: first, a new way to look at topical relevance, complementing the two dominant models, i.e., the classical probabilistic model and the language modeling approach, and which explicitly combines documents, queries, and relevance in a single formalism; second, a new method for modeling exchangeable sequences of discrete random variables which does not make any structural assumptions about the data and which can also handle rare events. Thus his book is of major interest to researchers and graduate students in information retrieval who specialize in relevance modeling, ranking algorithms, and language modeling.
## Grundbegriffe der Wahrscheinlichkeitsrechnung

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
## Philosophischer Versuch über die Wahrscheinlichkeit

## Theory of Stochastic Objects

This book defines and investigates the concept of a random object. To accomplish this task in a natural way, it brings together three major areas; statistical inference, measure-theoretic probability theory and stochastic processes. This point of view has not been explored by existing textbooks; one would need material on real analysis, measure and probability theory, as well as stochastic processes - in addition to at least one text on statistics- to capture the detail and depth of material that has gone into this volume. Presents and illustrates ‘random objects’ in different contexts, under a unified framework, starting with rudimentary results on random variables and random sequences, all the way up to stochastic partial differential equations. Reviews rudimentary probability and introduces statistical inference, from basic to advanced, thus making the transition from basic statistical modeling and estimation to advanced topics more natural and concrete. Compact and comprehensive presentation of the material that will be useful to a reader from the mathematics and statistical sciences, at any stage of their career, either as a graduate student, an instructor, or an academician conducting research and requiring quick references and examples to classic topics. Includes 378 exercises, with the solutions manual available on the book's website. 121 illustrative examples of the concepts presented in the text (many including multiple items in a single example). The book is targeted towards students at the master’s and Ph.D. levels, as well as, academicians in the mathematics, statistics and related disciplines. Basic knowledge of calculus and matrix algebra is required. Prior knowledge of probability or measure theory is welcomed but not necessary.
## Learning Data Mining with R

This book is intended for the budding data scientist or quantitative analyst with only a basic exposure to R and statistics. This book assumes familiarity with only the very basics of R, such as the main data types, simple functions, and how to move data around. No prior experience with data mining packages is necessary; however, you should have a basic understanding of data mining concepts and processes.
## Applied Statistical Genetics with R

Statistical genetics has become a core course in many graduate programs in public health and medicine. This book presents fundamental concepts and principles in this emerging field at a level that is accessible to students and researchers with a first course in biostatistics. Extensive examples are provided using publicly available data and the open source, statistical computing environment, R.
## Modeling Techniques in Predictive Analytics with Python and R

Master predictive analytics, from start to finish Start with strategy and management Master methods and build models Transform your models into highly-effective code—in both Python and R This one-of-a-kind book will help you use predictive analytics, Python, and R to solve real business problems and drive real competitive advantage. You’ll master predictive analytics through realistic case studies, intuitive data visualizations, and up-to-date code for both Python and R—not complex math. Step by step, you’ll walk through defining problems, identifying data, crafting and optimizing models, writing effective Python and R code, interpreting results, and more. Each chapter focuses on one of today’s key applications for predictive analytics, delivering skills and knowledge to put models to work—and maximize their value. Thomas W. Miller, leader of Northwestern University’s pioneering program in predictive analytics, addresses everything you need to succeed: strategy and management, methods and models, and technology and code. If you’re new to predictive analytics, you’ll gain a strong foundation for achieving accurate, actionable results. If you’re already working in the field, you’ll master powerful new skills. If you’re familiar with either Python or R, you’ll discover how these languages complement each other, enabling you to do even more. All data sets, extensive Python and R code, and additional examples available for download at http://www.ftpress.com/miller/ Python and R offer immense power in predictive analytics, data science, and big data. This book will help you leverage that power to solve real business problems, and drive real competitive advantage. Thomas W. Miller’s unique balanced approach combines business context and quantitative tools, illuminating each technique with carefully explained code for the latest versions of Python and R. If you’re new to predictive analytics, Miller gives you a strong foundation for achieving accurate, actionable results. If you’re already a modeler, programmer, or manager, you’ll learn crucial skills you don’t already have. Using Python and R, Miller addresses multiple business challenges, including segmentation, brand positioning, product choice modeling, pricing research, finance, sports, text analytics, sentiment analysis, and social network analysis. He illuminates the use of cross-sectional data, time series, spatial, and spatio-temporal data. You’ll learn why each problem matters, what data are relevant, and how to explore the data you’ve identified. Miller guides you through conceptually modeling each data set with words and figures; and then modeling it again with realistic code that delivers actionable insights. You’ll walk through model construction, explanatory variable subset selection, and validation, mastering best practices for improving out-of-sample predictive performance. Miller employs data visualization and statistical graphics to help you explore data, present models, and evaluate performance. Appendices include five complete case studies, and a detailed primer on modern data science methods. Use Python and R to gain powerful, actionable, profitable insights about: Advertising and promotion Consumer preference and choice Market baskets and related purchases Economic forecasting Operations management Unstructured text and language Customer sentiment Brand and price Sports team performance And much more
## Proceedings of the Section on Bayesian Statistical Science

## Wahrscheinlichkeitsrechnung und Statistik

Das Buch ist eine Einführung in die Wahrscheinlichkeitsrechnung und mathematische Statistik auf mittlerem mathematischen Niveau. Die Pädagogik der Darstellung unterscheidet sich in wesentlichen Teilen – Einführung der Modelle für unabhängige und abhängige Experimente, Darstellung des Suffizienzbegriffes, Ausführung des Zusammenhanges zwischen Testtheorie und Theorie der Bereichschätzung, allgemeine Diskussion der Modellentwicklung – erheblich von der anderer vergleichbarer Lehrbücher. Die Darstellung ist, soweit auf diesem Niveau möglich, mathematisch exakt, verzichtet aber bewußt und ebenfalls im Gegensatz zu vergleichbaren Texten auf die Erörterung von Meßbarkeitsfragen. Der Leser wird dadurch erheblich entlastet, ohne daß wesentliche Substanz verlorengeht. Das Buch will allen, die an der Anwendung der Statistik auf solider Grundlage interessiert sind, eine Einführung bieten, und richtet sich an Studierende und Dozenten aller Studienrichtungen, für die mathematische Statistik ein Werkzeug ist.
## Dynamic Linear Models with R

State space models have gained tremendous popularity in recent years in as disparate fields as engineering, economics, genetics and ecology. After a detailed introduction to general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. Whenever possible it is shown how to compute estimates and forecasts in closed form; for more complex models, simulation techniques are used. A final chapter covers modern sequential Monte Carlo algorithms. The book illustrates all the fundamental steps needed to use dynamic linear models in practice, using R. Many detailed examples based on real data sets are provided to show how to set up a specific model, estimate its parameters, and use it for forecasting. All the code used in the book is available online. No prior knowledge of Bayesian statistics or time series analysis is required, although familiarity with basic statistics and R is assumed.

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ISBN: 9780993367946

Category: Mathematics

Page: 186

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