Bayesian Probability Theory Download Ebook PDF Epub Online

Author : Wolfgang von der Linden
Volker Dose
Publisher : Cambridge University Press
Release : 2014-06-12
Page : 649
Category : Mathematics
ISBN 13 : 1107035902
Description :


Covering all aspects of probability theory, statistics and data analysis from a Bayesian perspective for graduate students and researchers.


Author : Wolfgang von der Linden. Volker Dose. Udo von Toussaint
Publisher :
Release : 2014
Page :
Category :
ISBN 13 : 9781139949293
Description :



Author : J. A. Hartigan
Publisher : Springer Science & Business Media
Release : 2012-12-06
Page : 146
Category : Mathematics
ISBN 13 : 1461382424
Description :


This book is based on lectures given at Yale in 1971-1981 to students prepared with a course in measure-theoretic probability. It contains one technical innovation-probability distributions in which the total probability is infinite. Such improper distributions arise embarras singly frequently in Bayes theory, especially in establishing correspondences between Bayesian and Fisherian techniques. Infinite probabilities create interesting complications in defining conditional probability and limit concepts. The main results are theoretical, probabilistic conclusions derived from probabilistic assumptions. A useful theory requires rules for constructing and interpreting probabilities. Probabilities are computed from similarities, using a formalization of the idea that the future will probably be like the past. Probabilities are objectively derived from similarities, but similarities are sUbjective judgments of individuals. Of course the theorems remain true in any interpretation of probability that satisfies the formal axioms. My colleague David Potlard helped a lot, especially with Chapter 13. Dan Barry read proof. vii Contents CHAPTER 1 Theories of Probability 1. 0. Introduction 1 1. 1. Logical Theories: Laplace 1 1. 2. Logical Theories: Keynes and Jeffreys 2 1. 3. Empirical Theories: Von Mises 3 1. 4. Empirical Theories: Kolmogorov 5 1. 5. Empirical Theories: Falsifiable Models 5 1. 6. Subjective Theories: De Finetti 6 7 1. 7. Subjective Theories: Good 8 1. 8. All the Probabilities 10 1. 9. Infinite Axioms 11 1. 10. Probability and Similarity 1. 11. References 13 CHAPTER 2 Axioms 14 2. 0. Notation 14 2. 1. Probability Axioms 14 2. 2.


Author : Wan-Huan Zhou
Zhen-Yu Yin
Publisher : Springer Nature
Release : 2020-11-13
Page : 324
Category : Science
ISBN 13 : 9811591059
Description :


This book introduces systematically the application of Bayesian probabilistic approach in soil mechanics and geotechnical engineering. Four typical problems are analyzed by using Bayesian probabilistic approach, i.e., to model the effect of initial void ratio on the soil–water characteristic curve (SWCC) of unsaturated soil, to select the optimal model for the prediction of the creep behavior of soft soil under one-dimensional straining, to identify model parameters of soils and to select constitutive model of soils considering critical state concept. This book selects the simple and easy-to-understand Bayesian probabilistic algorithm, so that readers can master the Bayesian method to analyze and solve the problem in a short time. In addition, this book provides MATLAB codes for various algorithms and source codes for constitutive models so that readers can directly analyze and practice. This book is useful as a postgraduate textbook for civil engineering, hydraulic engineering, transportation, railway, engineering geology and other majors in colleges and universities, and as an elective course for senior undergraduates. It is also useful as a reference for relevant professional scientific researchers and engineers.


Author : José M. Bernardo
Adrian F. M. Smith
Publisher : John Wiley & Sons
Release : 2009-09-25
Page : 608
Category : Mathematics
ISBN 13 : 047031771X
Description :


This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics


Author : Christopher Bowman
Publisher :
Release : 2016
Page :
Category :
ISBN 13 :
Description :



Author : E. T. Jaynes
Publisher : Cambridge University Press
Release : 2003-04-10
Page : 727
Category : Mathematics
ISBN 13 : 9780521592710
Description :


index


Author : P.F. Fougère
Publisher : Springer Science & Business Media
Release : 2012-12-06
Page : 490
Category : Mathematics
ISBN 13 : 9400906838
Description :


This volume represents the proceedings of the Ninth Annual MaxEnt Workshop, held at Dartmouth College in Hanover, New Hampshire, on August 14-18, 1989. These annual meetings are devoted to the theory and practice of Bayesian Probability and the Maximum Entropy Formalism. The fields of application exemplified at MaxEnt '89 are as diverse as the foundations of probability theory and atmospheric carbon variations, the 1987 Supernova and fundamental quantum mechanics. Subjects include sea floor drug absorption in man, pressures, neutron scattering, plasma equilibrium, nuclear magnetic resonance, radar and astrophysical image reconstruction, mass spectrometry, generalized parameter estimation, delay estimation, pattern recognition, heave responses in underwater sound and many others. The first ten papers are on probability theory, and are grouped together beginning with the most abstract followed by those on applications. The tenth paper involves both Bayesian and MaxEnt methods and serves as a bridge to the remaining papers which are devoted to Maximum Entropy theory and practice. Once again, an attempt has been made to start with the more theoretical papers and to follow them with more and more practical applications. Papers number 29, 30 and 31, by Kesaven, Seth and Kapur, represent a somewhat different, perhaps even "unorthodox" viewpoint, and are included here even though the editor and, indeed many in the audience at Dartmouth, disagreed with their content. I feel that scientific disagreements are essential in any developing field, and often lead to a deeper understanding.


Author : Will Kurt
Publisher : No Starch Press
Release : 2019
Page : 268
Category : Bayesian statistical decision theory
ISBN 13 : 1593279566
Description :


Bayesian Statistics the Fun Way gets you understanding the theory behind data analysis without making you slog through a load of dry concepts first - with no programming experience necessary. You'll learn about probability with LEGO, statistics through Star Wars, distributions with bomb fuses, estimation through precipitation, and come away with some strong mathematical reasoning skills. This is a super approachable book for people who need to do data science and probability work in their lives, but never got a good grip on the underlying theory.


Author : Phil Gregory
Publisher : Cambridge University Press
Release : 2005-04-14
Page :
Category : Mathematics
ISBN 13 : 113944428X
Description :


Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.


Author : Mike Oaksford
Nick Chater
Publisher : Oxford University Press
Release : 2007-02-22
Page : 330
Category : Philosophy
ISBN 13 : 9780198524496
Description :


For almost 2,500 years, the Western concept of what is to be human has been dominated by the idea that the mind is the seat of reason - humans are, almost by definition, the rational animal. In this text a more radical suggestion for explaining these puzzling aspects of human reasoning is put forward.


Author : Brendon James Brewer
Publisher :
Release : 2008
Page : 166
Category : Astrophysics
ISBN 13 :
Description :



Author : Sharon Bertsch McGrayne
Publisher : Yale University Press
Release : 2011-05-17
Page : 335
Category : Mathematics
ISBN 13 : 0300175094
Description :


"This account of how a once reviled theory, Baye’s rule, came to underpin modern life is both approachable and engrossing" (Sunday Times). A New York Times Book Review Editors’ Choice Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the generations-long human drama surrounding it. McGrayne traces the rule’s discovery by an 18th century amateur mathematician through its development by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—while practitioners relied on it to solve crises involving great uncertainty and scanty information, such as Alan Turing's work breaking Germany's Enigma code during World War II. McGrayne also explains how the advent of computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.


Author : Andrew Gelman
John B. Carlin
Publisher : CRC Press
Release : 2013-11-01
Page : 675
Category : Mathematics
ISBN 13 : 1439840954
Description :


Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.


Author : Suzette C. Lizamore
Publisher :
Release : 1995
Page : 68
Category : Bayesian statistical decision theory
ISBN 13 :
Description :



Author : Chris Ferrie
Publisher : Sourcebooks, Inc.
Release : 2019-07-02
Page : 24
Category : Juvenile Nonfiction
ISBN 13 : 1728213517
Description :


Fans of Chris Ferrie's Rocket Science for Babies, Astrophysics for Babies, and 8 Little Planets will love this introduction to the basic principles of probability for babies and toddlers! Help your future genius become the smartest baby in the room! It only takes a small spark to ignite a child's mind. If you took a bite out of a cookie and that bite has no candy in it, what is the probability that bite came from a candy cookie or a cookie with no candy? You and baby will find out the probability and discover it through different types of distribution. Yet another Baby University board book full of simple explanations of complex ideas written by an expert for your future genius! If you're looking for baby math books, probability for kids, or more Baby University board books to surprise your little one, look no further! Bayesian Probability for Babies offers fun early learning for your little scientist!


Author : Michael Havbro Faber
Publisher : Springer Science & Business Media
Release : 2012-03-23
Page : 192
Category : Technology & Engineering
ISBN 13 : 9400740565
Description :


This book provides the reader with the basic skills and tools of statistics and probability in the context of engineering modeling and analysis. The emphasis is on the application and the reasoning behind the application of these skills and tools for the purpose of enhancing decision making in engineering. The purpose of the book is to ensure that the reader will acquire the required theoretical basis and technical skills such as to feel comfortable with the theory of basic statistics and probability. Moreover, in this book, as opposed to many standard books on the same subject, the perspective is to focus on the use of the theory for the purpose of engineering model building and decision making. This work is suitable for readers with little or no prior knowledge on the subject of statistics and probability.


Author : Fabrizia Guglielmetti
Publisher :
Release : 2010
Page : 242
Category :
ISBN 13 :
Description :



Author : Cameron Davidson-Pilon
Publisher : Addison-Wesley Professional
Release : 2015-09-30
Page : 256
Category : Computers
ISBN 13 : 0133902927
Description :


Master Bayesian Inference through Practical Examples and Computation–Without Advanced Mathematical Analysis Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You’ll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you’ve mastered these techniques, you’ll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes • Learning the Bayesian “state of mind” and its practical implications • Understanding how computers perform Bayesian inference • Using the PyMC Python library to program Bayesian analyses • Building and debugging models with PyMC • Testing your model’s “goodness of fit” • Opening the “black box” of the Markov Chain Monte Carlo algorithm to see how and why it works • Leveraging the power of the “Law of Large Numbers” • Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning • Using loss functions to measure an estimate’s weaknesses based on your goals and desired outcomes • Selecting appropriate priors and understanding how their influence changes with dataset size • Overcoming the “exploration versus exploitation” dilemma: deciding when “pretty good” is good enough • Using Bayesian inference to improve A/B testing • Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.


Author : Jim Albert
Jingchen Hu
Publisher : CRC Press
Release : 2019-12-06
Page : 538
Category : Mathematics
ISBN 13 : 1351030132
Description :


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.