Our wonderful new Bayesian Workflow book is now available as a free pdf! Just go the link—it’s right there!
I recommend getting the hard copy too because you’ll want to be able to read it while working on the computer, and the cost of the book is trivial compared to the benefit from faster learning that you will get by being able look at the book without taking up valuable screen real estate; also you can see connections when flipping through the pages that might not be apparent by viewing one page at a time on a screen.
Conversely, if you have the hard copy, you should still download the pdf because it fixes a bunch of minor errors that we caught after the book went to press. Also in the printed version we accidentally repeated some of the exercises in chapters 2 and 3. For the pdf we fixed this.
Regarding the content, as I wrote last month, with Bayesian Data Analysis, the big steps forward were:
- Going beyond Bayesian inference to also consider Bayesian model building (as a researcher, you construct the model, it isn’t just given to you as in a textbook), model checking (breaking through the absolutely horrible attitude, common to Bayesians in the early 1990s, that the model was “subjective” and thus should not be checked), and model improvement (continuous model expansion, not the misguided idea of assigning posterior probabilities).
- Going beyond simple conjugate models. BDA had lots of hierarchical models, also lots of computational tools so that you could fit the models you want by putting them together from understandable components. And I like how we had a clear separation between modeling and computing. The model comes first, then you figure out how to compute it. Or you set up a model that works within your computational constraints.
- A Bayesian approach to sampling and causal inference. This was Rubin’s framework in which unobserved units in the population and unobserved causal outcomes are treated as missing data and are part of a joint probability model. We worked this out in chapter 7 of BDA (which became chapter 8 in the third edition of the book).
- Lots of live examples. Not just “real-data examples,” but problems we’d directly worked on. This motivated us and I think it gave our readers a sense of how Bayesian methods worked not just in theory but in applied problems.
- A pragmatic view of probability as a measurable quantity. That’s right there in chapter 1. Bayesian methods are not the product of a philosophical stance; they’re a way to connect models and data using probability.
I could go on and on, but for that I can refer you to the Bayesian Data Analysis book.
And these are the key innovations of Bayesian Workflow:
- Going beyond Bayesian data analysis (model building, inference, model checking, and model expansion) to consider the larger process of statistical modeling, including comparisons of multiple models fit to a single dataset.
- A fuller use of informative priors. This is a big deal. In BDA we still had a bit of the Bayesian cringe going on. One reason we’ve moved toward stronger priors is that the replication crisis has taught us that the amount of prior information available in any given problem is often approximately the same as the information coming from an experiment (see here, for example). Informative priors also fit our increased focus on generative modeling, and we’re doing a lot more prior predictive checking to understand the implications of our models.
- More integration between modeling, data analysis, and computing. One way to see this is that the Bayesian Workflow webpage has the code to run all our examples. We also have lots of code snippets in the text as a way of demonstrating the way in which coding is central to our statistical workflow.
- Lots more live examples. It’s been 30 years since BDA first came out. One reason that Bayesian Workflow has 11 authors is that different collaborators worked on different examples (but the three principal authors read through the entire book, so the general approach should remain coherent).
- Simulation-based experimentation. This is something my colleagues have been doing more and more over the years. At its most basic, simulation-based experimentation provides a best-case baseline for statistical methods: if you can’t recover your quantities of interest with sufficient accuracy under ideal conditions (when your data are simulated from the model you’re fitting), then you know you’re in trouble. And often this is the case! Beyond that, we can simulate from one model and fit another, and see what happens. Simulation experiments aren’t always so easy to construct, as they involve specifying the entire data-generation process. But we think this is effort worth expending, as it involves thinking about the problem you’re working on.
I could go on and on, but for that I can refer you to the Bayesian Workflow book.