An Introduction to Bayesian Scientific Computing PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download An Introduction to Bayesian Scientific Computing PDF full book. Access full book title An Introduction to Bayesian Scientific Computing by Daniela Calvetti. Download full books in PDF and EPUB format.
Author: Daniela Calvetti
Publisher: Springer Science & Business Media
ISBN: 0387733949
Category : Computers
Languages : en
Pages : 202
Get Book Here
Book Description
This book has been written for undergraduate and graduate students in various disciplines of mathematics. The authors, internationally recognized experts in their field, have developed a superior teaching and learning tool that makes it easy to grasp new concepts and apply them in practice. The book’s highly accessible approach makes it particularly ideal if you want to become acquainted with the Bayesian approach to computational science, but do not need to be fully immersed in detailed statistical analysis.
Author: Daniela Calvetti
Publisher: Springer Science & Business Media
ISBN: 0387733949
Category : Computers
Languages : en
Pages : 202
Get Book Here
Book Description
This book has been written for undergraduate and graduate students in various disciplines of mathematics. The authors, internationally recognized experts in their field, have developed a superior teaching and learning tool that makes it easy to grasp new concepts and apply them in practice. The book’s highly accessible approach makes it particularly ideal if you want to become acquainted with the Bayesian approach to computational science, but do not need to be fully immersed in detailed statistical analysis.
Author: Jun S. Liu
Publisher: Springer Science & Business Media
ISBN: 0387763716
Category : Mathematics
Languages : en
Pages : 350
Get Book Here
Book Description
This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.
Author: Daniela Calvetti
Publisher: Springer Nature
ISBN: 3031238249
Category : Computers
Languages : en
Pages : 295
Get Book Here
Book Description
The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider’s view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas.
Author: Cameron Davidson-Pilon
Publisher: Addison-Wesley Professional
ISBN: 0133902927
Category : Computers
Languages : en
Pages : 551
Get Book Here
Book 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: Osvaldo A. Martin
Publisher: CRC Press
ISBN: 1000520048
Category : Business & Economics
Languages : en
Pages : 421
Get Book Here
Book Description
Bayesian Modeling and Computation in Python aims to help beginner Bayesian practitioners to become intermediate modelers. It uses a hands on approach with PyMC3, Tensorflow Probability, ArviZ and other libraries focusing on the practice of applied statistics with references to the underlying mathematical theory. The book starts with a refresher of the Bayesian Inference concepts. The second chapter introduces modern methods for Exploratory Analysis of Bayesian Models. With an understanding of these two fundamentals the subsequent chapters talk through various models including linear regressions, splines, time series, Bayesian additive regression trees. The final chapters include Approximate Bayesian Computation, end to end case studies showing how to apply Bayesian modelling in different settings, and a chapter about the internals of probabilistic programming languages. Finally the last chapter serves as a reference for the rest of the book by getting closer into mathematical aspects or by extending the discussion of certain topics. This book is written by contributors of PyMC3, ArviZ, Bambi, and Tensorflow Probability among other libraries.
Author: William M. Bolstad
Publisher: John Wiley & Sons
ISBN: 1118593227
Category : Mathematics
Languages : en
Pages : 608
Get Book Here
Book Description
"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.
Author: Peter M. Lee
Publisher: Wiley
ISBN: 9780340814055
Category : Mathematics
Languages : en
Pages : 352
Get Book Here
Book Description
Bayesian Statistics is the school of thought that uses all information surrounding the likelihood of an event rather than just that collected experimentally. Among statisticians the Bayesian approach continues to gain adherents and this new edition of Peter Lee’s well-established introduction maintains the clarity of exposition and use of examples for which this text is known and praised. In addition, there is extended coverage of the Metropolis-Hastings algorithm as well as an introduction to the use of BUGS (Bayesian Inference Using Gibbs Sampling) as this is now the standard computational tool for such numerical work. Other alterations include new material on generalized linear modelling and Bernardo’s theory of reference points.
Author: Ben Klemens
Publisher: Princeton University Press
ISBN: 1400828740
Category : Mathematics
Languages : en
Pages : 471
Get Book Here
Book Description
Modeling with Data fully explains how to execute computationally intensive analyses on very large data sets, showing readers how to determine the best methods for solving a variety of different problems, how to create and debug statistical models, and how to run an analysis and evaluate the results. Ben Klemens introduces a set of open and unlimited tools, and uses them to demonstrate data management, analysis, and simulation techniques essential for dealing with large data sets and computationally intensive procedures. He then demonstrates how to easily apply these tools to the many threads of statistical technique, including classical, Bayesian, maximum likelihood, and Monte Carlo methods. Klemens's accessible survey describes these models in a unified and nontraditional manner, providing alternative ways of looking at statistical concepts that often befuddle students. The book includes nearly one hundred sample programs of all kinds. Links to these programs will be available on this page at a later date. Modeling with Data will interest anyone looking for a comprehensive guide to these powerful statistical tools, including researchers and graduate students in the social sciences, biology, engineering, economics, and applied mathematics.
Author: Andrew Gelman
Publisher: CRC Press
ISBN: 1439840954
Category : Mathematics
Languages : en
Pages : 677
Get Book Here
Book 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: Phil Gregory
Publisher: Cambridge University Press
ISBN: 113944428X
Category : Mathematics
Languages : en
Pages : 498
Get Book Here
Book 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.
