Vehtari group: consistent priors can replace Bayesian model selection

A new Bayesian methods paper, posted to arXiv on June 22 2026 by Anna Elisabeth Riha, Leevi Lindgren, David Kohns, Paul-Christian Bürkner and Aki Vehtari, makes a claim that cuts against the usual workflow advice: if your priors are set up right, you may not need to do model selection at all. The paper is titled 'To select or not to select: predictively consistent priors instead of model selection.'

The argument, as stated in the abstract, is that 'flexible models with predictively consistent priors typically match or outperform selected simpler models in out-of-sample predictive performance.' A predictively consistent prior, in the authors' framing, is one whose implications in predictive space remain stable as model complexity grows. The stronger claim sits underneath: when model selection does visibly help, that is a signal something is wrong with your priors, not a sign you have found the right model.

For people who build Bayesian models day to day, this is a meaningful re-framing if it holds. A lot of the Bayesian workflow as taught involves fitting a ladder of nested or competing models, then using something like cross validation or information criteria to pick one. The paper is saying that ceremony may be doing less work than people think, and that effort is better spent on prior specification within a single flexible model. The authors report testing across linear and logistic regression, variable selection, and nonlinear modeling.

The honest caveat is that this is a sweeping methodological claim and the demonstrations live in fairly classical regression-style settings. What the posting does not give you, at least not from the abstract, is a recipe for constructing predictively consistent priors in a model class you have never worked with before, or evidence that the result extends to large hierarchical models or neural-network-style architectures. The paper itself is 34 pages plus 36 of supplementary material, so the detail is there for anyone who wants to read into it.

If the framework lands with practitioners, the people best positioned to benefit are applied modelers who currently spend more time on selection than on thinking about priors, and the maintainers of probabilistic programming tooling who could ship diagnostics that bake the idea in. The direction worth watching is whether follow-up work shows the same effect outside the regression sandbox.