Introduction
I provide below a list of books that I have read and found useful. They differ substantially regarding the emphasis that they put on different things. For example:
some of these books focus much more in implementation whereas others focus more on theory;
some books include WinBUGS/JAGS/Nimble code, others focus on using R packages, others build Bayesian models from scratch, and others do not include any code whatsoever.
some books require a good understanding of probability theory and/or linear algebra while others do not.
For this reason, I have tried to provide short comments besides each book to give a sense of what people should expect from them.
Books on important statistical concepts (e.g., maximum likelihood, distributions, and non-linear deterministic functions)
Hilborn, R.; Mangel, M. 1997. The ecological detective: confronting models with data. Princeton University Press. (Does not include code)
Bolker, B. 2008. Ecological models and data in R. Princeton University Press. (Includes R code)
Gelman, A.; Hill, J. 2007. Data analysis using regression and multilevel/hierarchical models. Cambridge University press. (Heavily focused on models with random effects [i.e., mixed models]. Includes code in R and WinBUGS)
Introductory books on Bayesian statistics
Winkler, R. 2003. An introduction to Bayesian inference and decision (2nd edition). Probabilistic Publishing. (Focused on problems that can be solved with paper and pencil and decision making problems in the presence of uncertainty. Does not include code)
Gelman, A.; Carlin, J. B.; Stern, H. S.; Rubin, D. B. 2004. Bayesian data analysis (2nd edition). CRC Press (This is a more technical book. Does not include code)
McCarthy, M. A. 2007. Bayesian methods for Ecology. Cambridge University press. (Focused on ecological examples. Includes WinBUGS/JAGS/NIMBLE code)
Hoff, P. 2009. A first course in Bayesian statistical methods. Springer. (Focused on programming Gibbs samplers from scratch in R. Includes R code. Requires readers to be somewhat comfortable with linear algebra.)
McElreath, R. 2020. Statistical rethinking: a Bayesian course with examples in R and Stan (2nd edition). CRC press. (Includes code in R and STAN)
More advanced material on statistics
Denison, D. G. T.; Holmes, C. C.; Mallick, B. K.; Smith, A. F. M. 2004. Bayesian methods for nonlinear classification and regression. John Wiley & Sons. (Focuses on Bayesian model averaging and model selection. Requires readers to be comfortable with linear algebra. Does not include code.)
Wood. 2017. Generalized additive models: an introduction with R (2nd edition). CRC Press. (Heavily focused on splines as a way to extend standard regression models. Requires readers to be comfortable with linear algebra. Include R code.)
Kery, M.; Schaub, M. 2012. Bayesian population analysis using WinBUGS: a hierarchical perspective. Academic press. (Focused on models for different types of wildlife data. Includes WinBUGS/JAGS/NIMBLE code)
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