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The ABS Bayesian Priors Framework (Agnostic, Believer, Skeptic)
Our paper Choosing informative priors in Bayesian regression models, is out in Frontiers in Psychology. It is a simulation study and a hands-on tutorial in R and Stan, but the part I want to emphasize here is the small conceptual move underneath it, because I think it addresses something that has bothered me about how we talk about priors.
The idea has been sitting in a bayestestR discussion thread since 2019. The starting point was practical: most people who fit Bayesian models leave the default priors on, not because they think defaults are right but because specifying anything else feels like an exam they did not revise for. Which distribution? Centred where? How wide? Most guides and resources answer with the same three words: use weakly informative priors. And every reader is left wondering what, exactly, that means for their model.
The problem with "informative"
The usual vocabulary sorts priors on a single axis. Non-informative or flat at one end, weakly informative in the middle, informative at the other. It sounds like a dial from "let the data speak" to "impose my beliefs", and that is how it is often taught. But the axis quietly bundles together questions that have nothing to do with each other.
Consider a prior on a regression coefficient that is tightly concentrated around zero. Is it informative? It is extremely informative: it says the effect is almost certainly negligible. Yet the same prior is routinely called conservative, or sometimes uninformative, because it does not favour a direction. Now consider a very wide prior centred on the effect you expect from the literature. It carries real information (which way the effect points, and roughly how big it might be), but it barely constrains the posterior. Informative or not? The "informative vs. non-informative" framework tries to describe two different things at once: where the prior is centred and how tightly it holds.
The ABS Priors Framework (Agnostic, Believer, Skeptic)
The framework we use in the paper separates the choice into two orthogonal main dimensions.
1. Location: where does the prior sit relative to the effect you expect? This is where the three labels come in. A believer prior is centred on the effect the literature or theory leads you to expect, which can be useful with noisy evidence or to help with sampling. An agnostic prior is centred on zero: no effect until the data say otherwise. A skeptic prior is centred on the opposite of the expected effect, and exists to stress-test a result or steelman an argument: if the effect survives a prior that actively bets against it, it is not an artefact of your optimism. The paper is careful about one thing, and so am I: these names describe the position of a distribution, not the attitude of the analyst. Running a skeptic prior does not make you a skeptic. It makes you thorough.
2. Precision: how tightly does the prior hold that position? Flat, wide, narrow, very narrow. This is the dimension the word "informative" often implicitly refers to: how much do I trust the location, and how much shrinkage am I willing to apply? A narrow believer prior and a narrow agnostic prior are equally "informative"; they just inform in opposite directions.
There is a further dimension, which could be seen as a third dimension: the shape, or type, of the distribution. Some priors are fundamentally incompatible with the parameter they are placed on. A normal distribution on a standard deviation, which can only be positive, puts half of its mass on values that cannot exist; a prior on a probability that spills outside 0 and 1 does the same. Such a prior is malformed whatever its location and precision, and no amount of tuning the two other dials will repair it. The family has to match the geometry of the parameter first; only then do location and precision mean anything.
But why?
In this framework, a lot of muddled advice becomes clear. "Conservative" is not the same as "uninformative": a narrow agnostic prior is a strong claim. A wide believer prior is not cheating; it is a gentle nudge that the data will override with modest sample sizes. And the three locations, run side by side, give you a sensitivity analysis for free: report the believer, agnostic and skeptic posteriors together, and the reader sees at a glance how much of the conclusion is data and how much is prior.
The paper shows both halves of this. The simulation varies location and scale across sample sizes for a known true effect, and the result is the one you would hope for: priors pull hardest when N is small, and as the sample grows the likelihood takes over and every prior converges on the truth. Then a case–control study of falls in dementia patients (N = 526) shows why you would want that pull. Severe dementia and falls co-occur rarely enough in the data that a classical logistic regression returns an odds ratio of 8.87 with a confidence interval from 1.66 to 165: technically significant, practically meaningless. A moderately narrow believer prior derived from earlier studies gives an odds ratio of 4.01 with a credible interval from 1.99 to 8.78. The agnostic and skeptic priors are reported alongside, so nobody has to take the believer's word for it.
How to use priors in practice
- Shape first: Make sure the prior distribution fits the parameter space.
- Then location: say out loud whether you are a believer, an agnostic or a skeptic about this parameter, and centre the prior accordingly.
- Then precision: choose a scale, and check it with prior predictive checks: does the model, before seeing data, generate outcomes that look like the world?
- Ideally, report the other two locations as a sensitivity analysis (it costs two more model fits).
