Bayesian data analysis
"Bayesian Data Analysis is a comprehensive treatment of the statistical analysis of data from a Bayesian perspective. Modern computational tools are emphasized, and inferences are typically obtained using computer simulations.". "The principles of Bayesian analysis are described with an emphasis on practical rather than theoretical issues, and illustrated using actual data. A variety of models are considered, including linear regression, hierarchical (random effects) models, robust models, generalized linear models and mixture models.". "Two important and unique features of this text are thorough discussions of the methods for checking Bayesian models and the role of the design of data collection in influencing Bayesian statistical analysis." "Issues of data collection, model formulation, computation, model checking and sensitivity analysis are all considered. The student or practising statistician will find that there is guidance on all aspects of Bayesian data analysis."--BOOK JACKET.
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- The textbook, "Bayesian Data Analysis" by Gelman et al, has a good discussion on this in Chapter 8. Here are some relevant bits:
"A naive student of Bayesian inference might claim that because all inference is conditional on the observed data, it makes no difference how those data were collected. This misplaced appeal to the likelihood principle would assert that given (1) a fixed model (including the prior distribution) for the underlying data and (2) fixed observed values of the data, Bayesian inference is determined regardless of the design for the collection of the data. Under this view there would be no formal role for randomization in either sample surveys or experiments."
"The notion that the method of data collection is irrelevant to Bayesian analysis can be dispelled by the simplest of examples. Suppose for instance that we, the authors, give you, the reader, a collection of the outcomes of ten rolls of a die and all are 6's. Certainly your attitude toward the nature of the die after analyzing these data would be different if we told you (i) these were the only rolls we performed, versus (ii) we rolled the die 60 times but decided to report only the 6's, versus (iii) we decided in advance that we were going to report honestly that ten 6's appeared but would conceal how many rolls it took, and we had to wait 500 rolls to attain that result."
- I think Bayesian Data Analysis is the natural progression step.
Not sure if there is a more recent book that's updated to use modern Stan examples, but the Stan user guide itself has developed into a very useful resource on its own. It contains a large number of example models and builds up concepts incrementally. The writing style is also generally easy to follow.
- Check out Bayesian Data Analysis by Gelman too. BDA and MLAPP are my go to resources for anything Bayesian.
- I usually enjoy reading something thick and technical during my summer vacation, to learn something new and not necessarily work-related. This year, however, I am not sure which book to pick up. I would love to see what's on your summer reading lists.
My recent favourites:
Bayesian Data Analysis, 3rd ed, by Gelman et al
Designing Data-Intensive Applications, by Martin Kleppmann
The Art of Electronics, by Horowitz & Hill
- Bayesian Data Analysis by Gelman et al. There's a free PDF available on Gelman's website [1]. Definitely application-focused, and the authors are a who's-who of contemporary Bayesian statisticians.
- Gelman's (one of the authors behind Stan) Bayesian Data Analysis is considered to be one of the best resources on this subject, so I suggest giving that a read. It's not the easiest book to work through though.
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