Bayesian Statistics with Stan

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Bayesian Statistics Using StanVersion 2.18Stan Development Team
About this Book

This book is is the official user’s guide for Stan. It provides example models and programming techniques for coding statistical models in Stan. It also serves as an example-driven introduction to Bayesian modeling and inference.

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关键词：Statistics statistic Bayesian Statist Statis

How to use this book
Part 1 introduces Bayesian data analysis and Stan through a series of examples.

Part 2 gives Stan code and discussions for several important classes of models.

Part 3 discusses various general Stan programming techniques that are not tied to any particular model.

Part 4 is a brief review of statistical inference.

The appendices provide a style guide and advice for users of BUGS and JAGS.

We recommend working through this book using the textbooks Bayesian Data Analysis and Statistical Rethinking: A Bayesian Course with Examples in R and Stan as references on the concepts, and using the Stan Reference Manual when necessary to clarify programming issues. Further resources are given at the end of the introductory chapter.

Additional Stan manuals and guides
In addition to this book, there are two reference manuals for the Stan language and algorithms. The Stan Reference Manual specifies the Stan programming language and inference algorithms. The Stan Functions Reference specifies the functions built into the Stan programming language.

There is also a separate installation and getting started guide for each of the Stan interfaces (R, Python, Julia, Stata, MATLAB, Mathematica, and command line).

Web resources
Stan is an open-source software project, resources for which are hosted on various web sites:

The Stan Web Site organizes all of the resources for the Stan project for users and developers. It contains links to the official Stan releases, source code, installation instructions, and full documentation, including the latest version of this manual, the user’s guide and the getting started guide for each interface, tutorials, case studies, and reference materials for developers.

The Stan Forums provide structured message boards for questions, discussion, and announcements related to Stan for both users and developers.

The Stan GitHub Organization hosts all of Stan’s code, documentation, wikis, and web site, as well as the issue trackers for bug reports and feature requests and interactive code review for pull requests.

Copyright, Trademark, and Licensing

This book is copyright 2011–2018, Stan Development Team and their assignees. The text content is distributed under the CC-BY ND 4.0 license. The user’s guide R and Stan programs are distributed under the BSD 3-clause license.

The Stan name and logo are registered trademarks of NumFOCUS. Use of the Stan name and logo are governed by the Stan logo usage guidelines.

Part 1: Bayesian Workflow

In this part of the book, we introduce the principles of Bayesian data analysis using Stan with straightforward examples.

Bayesian inference and Stan

Bayesian inference is a statistical power tool. You embed your data and unknowns in a probability model, and then you get a “posterior distribution” which you can use to make inferences and predictions about everything.

Stan is a platform for statistical modeling and high-performance statistical computation.

A big challenge for applied Bayesian inference is computation: converting the mathematical expression of the posterior distribution into specific inferences or predictions such as the posterior probability that some coefficient is positive, or a 90% predictive interval for some future outcome. For even moderately large or complex problems, such quantities are expressed mathematically in terms of high-dimensional integrals with no closed-form expressions.

Over the past fifty years, a series of advances in computational statistics have allowed these intergrals to be computed using approximations and simulations. The simulations use random numbers and are called “Monte Carlo methods,” named after the city in Europe that is famous for its gambling casinos. These methods were originally developed in the 1940s for aiding in large computations for the military, and in the 1980s it became clear how to apply them for general problems in Bayesian inference.

So: since the 1970s–1980s, methods have been developed to perform approximate computations for Bayesian inferences that would otherwise require intractable intervals. These approximations needed to be developed one model at a time. In the 1990s–2000s, the WinBugs software was developed, which allowed automatic computation for a large class of Bayesian models. WinBugs (and its successors, OpenBugs and Jags) can be slow, and starting in 2011 we developed Stan, which uses more efficient computations (Hamilton Monte Carlo, the no-U-turn sampler, and algorithmic autodifferentiation) so that automatic Bayesian computation can be applied to larger and more complex problems.

Where we stand now is that, for a fairly broad class of models and data of moderate size, we can transparently program our Bayesian models in Stan and perform inference automatically. This represent the culmination of decades of work in computational statistics, along with corresponding decades of experience fitting and understanding these models. The challenge is not just fitting the model; it is also deciding what models to fit.

Future work, by ourselves and others, will increase the speed and scalability of Stan in various ways, including more seamless implantation of parallel processing.

oliyiyi 发表于 2019-1-9 16:48
Bayesian Statistics Using StanVersion 2.18Stan Development Team
About this BookThis book is is the  ...

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