Bayesian Statistics: The three cultures

The author is claiming that Bayesians vary along two axes: (1) whether they generally try to inform their priors with their knowledge or beliefs about the world, and (2) whether they iterate on the functional form of the model based on its goodness-of-fit and the reasonableness and utility of its outputs. He then labels 3 of the 4 resulting combinations as follows:

    ┌───────────────┬───────────┬──────────────┐
    │               │ iteration │ no iteration │
    ├───────────────┼───────────┼──────────────┤
    │ informative   │ pragmatic │ subjective   │
    │ uninformative │     -     │ objective    │
    └───────────────┴───────────┴──────────────┘

My main disagreement with this model is the empty bottom-left box - in fact, I think that's where most self-labeled Bayesians in industry fall:

- Iterating on the functional form of the model (and therefore the assumed underlying data generating process) is generally considered obviously good and necessary, in my experience.

- Priors are usually uninformative or weakly informative, partly because data is often big enough to overwhelm the prior.

The need for iteration feels so obvious to me that the entire "no iteration" column feels like a straw man. But the author, who knows far more academic statisticians than I do, explicitly says that he had the same belief and "was shocked to learn that statisticians didn’t think this way."

Interesting, in my experience modern ML runs almost entirely on pragmatic Bayes. You find your ELBO, you choose the latest latent variable du jour that best models your problem domain (these days it's all transformers), and then you start running experiments.