Getting Through Applied Bayesian Statistics
The Cowles textbook has been around since the late 2000s and it shows. You can tell because some of the code examples still reference software versions that haven't existed for over a decade. The conceptual framework is solid, but working through it as a primary learning resource means you are going to run into friction at multiple points. That is fine. It is not the worst book out there, but it is not the most current either. The book covers prior specification, posterior computation, model checking, and decision theory with a strong emphasis on Gibbs sampling and Metropolis-Hastings algorithms. The chapters are arranged to build from conjugate families toward hierarchical models and model selection. If you are coming in with no Bayesian background, start with the earlier chapters on probability and likelihood before you get to the MCMC sections. The jump in difficulty around chapter 5 is real and the text does not soften it.
Applied Bayesian Statistics Mary Kathryn Cowles
What actually makes this book different from most introductory texts is the relentless focus on computation. Every concept is tied to an R implementation. That is useful if you want to leave the chapter knowing how to write the code. It is annoying if you just want the theory, because there is very little breathing room between the math and the program listing. You get both simultaneously, which is fine until you hit a bug in the code that does not match what the book shows, which happens more often than you would expect from a printed text. One concrete issue I ran into was when I was working through the hierarchical normal model example with a small group. The posterior sample sizes in the book assume you are running the sampler long enough to converge, but the default iteration counts in the companion code snippets fall well short for anything with weakly informative priors on variance components. I ended up doubling the burn-in and thinning intervals, and even then the effective sample size for the between-group variance was hovering around 200, which is basically unusable for any serious inference. The workaround was straightforward: switch to a non-centered parameterization for the hierarchy and use a half-Cauchy prior on the standard deviation instead of a flat prior. That stabilized the sampler considerably and pushed effective sample sizes above 1000 within reasonable wall-clock time. Here is something the book does not stress enough: most of the examples use Gibbs sampling because it is elegant and works cleanly with conjugate priors. In practice, conjugacy is rare outside of textbook exercises. When you move to real data with arbitrary likelihoods, Gibbs stops being an option and you are relying on Metropolis or Metropolis-within-Gibbs, and the tuning parameters for those algorithms make or break your run. The book introduces auto-correlation and convergence diagnostics, but it does not adequately prepare you for the moment when your chains look fine visually and the trace plots lie to you. I have seen multiple cases where the Gelman-Rubin statistic was below 1.1 but the chains were stuck in different modes of a multimodal posterior. Checking multiple random starts and inspecting the energy plot is more reliable than trusting a single diagnostic number.
The model comparison section is another area where the book oversimplifies. Deviance Information Criterion is presented almost as a drop-in replacement for cross-validation, which it is not. DIC penalizes model complexity in a particular way that assumes posterior normality, and that assumption breaks down in hierarchical settings with few groups. I switched to leave-one-out cross-validation with Pareto smoothed importance sampling when I needed actual predictive comparison, and it changed the preferred model in two separate projects where DIC and LOO disagreed. The book does not cover PSIS-LOO at all. If you are using this book to learn Bayesian methods, pair it with something more recent for the computational pieces. The R code is functional but the packages it references may need updating. The underlying statistics are sound and the exposition is generally clear. The gaps are in areas that have moved on since the book was written, particularly around variational inference, Stan-based workflows, and modern predictive validation techniques. You will get more out of the text if you treat it as a conceptual foundation and look elsewhere for the current implementation practices. The strongest chapters remain the ones on hierarchical modeling and the ones that walk through complete analysis pipelines from prior elicitation through posterior interpretation. Those sections read like someone actually sat down and thought about what a real analysis looks like. The weaker chapters are the ones that treat MCMC as a solved problem rather than a set of tools that require careful diagnosis at every step. Both perspectives exist in the same book, and knowing which is which when you open a given chapter will save you a lot of time.
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