Prior Compass — Bayes Thinking Lab

Before you pick concrete distributions in Prior Lab: why do you even need a prior, for which model parameter, and over what range of values does that make sense?

What is this about?

A prior is a statement about a specific parameter of your model, in its unit, with a plausible range of values. Until these three things are clear, any distribution choice in Prior Lab is guesswork: you can type in some Normal(0,1), but without knowing what this parameter means in your own study and what values it could even take, it stays unclear whether 0,1 is narrow, wide, plausible, or absurd.

A prior brings additional information into the model. That can range from fairly vague, regularizing, all the way to quite concrete, based on prior knowledge. Regularizing means it is fairly wide and doesn't favor a direction, so as to keep the model from drifting into completely implausible regions during MCMC sampling. At the other end of the spectrum are informed priors, which bring in real prior knowledge (from previous studies, meta-analyses, theory) and steer the estimate deliberately in a direction. You'll find worked examples of all of this in the Parameter Atlas.

The intercept β₀ describes the expected value of the DV when all predictors are zero. This is only meaningfully interpretable if "all predictors = 0" actually describes a real, plausible situation — for a binary 0/1 predictor that's usually the case, but for a metric predictor with a purely positive range far from zero (e.g. study time in hours) it often isn't: an intercept at "0 hours studied" always technically exists, but substantively it's an extrapolation far outside the observed data. That's why centering is often useful for metric predictors: subtract the predictor's mean, and the intercept then describes the expected value at an average (rather than an often unrealistic zero) predictor value — a substantively more meaningful and easier-to-justify reference.

For slopes, an important special case applies: their plausible range depends both on the metric of the DV and on the metric of the predictor — never on just one of the two sides alone. The guiding question is always the same: By how many units does the DV change when I change the predictor by one unit? The same substantive relationship looks completely different in raw-score units than in z-standardized units — not because anything about the underlying effect changes, but because the scales on both sides of the equation change.

⚠ Important principle

A prior should reflect your current state of knowledge — not your wish for where the effect should lie! If nothing is known in this area yet, use a vague, regularizing prior centered on zero. If plausible restrictions can be justified without favoring a direction (see the IQ example for β₀, the intercept), that's sensible. Priors that point exactly in the direction of your preferred effect, without concrete, justified prior information (e.g. meta-analyses), are not an honest approach!

How to proceed

1. Parameter Atlas — a simple model equation, click through Intercept, Slopes and σ: what does each of these parameters control, what unit does it have, what range of values is plausible, and which distribution shape fits its natural boundary (e.g. σ must be positive, intercepts and slopes don't have to be)? The same question is worked through for three different outcome variables (IQ, z-score, BDI-II), so it becomes visible: the method of thinking about plausible ranges stays the same, only the concrete numbers change with the DV's scale.
2. GLM Link Scale — for Bernoulli/Poisson/Gamma, the prior lives on a different scale (η, the linear predictor) than what you actually observe and substantively interpret (probability, rate, mean). These two scales are connected by a non-linear link function — meaning: a prior that looks harmless and symmetric on η can behave completely differently on the response scale, sometimes very informative, sometimes distorted. Here you learn how to work backward from a substantive idea ("values between X% and Y%") to the matching model-scale distribution.
3. Decision Wizard — when you need a quick, first rough orientation: based on a few questions (type of outcome, parameter type, your plausibility judgment), it suggests a concrete prior distribution — including alternatives (e.g. Student-t instead of Normal, so as not to rule out extreme values too hard) and a direct deep link into Prior Lab. The wizard does NOT replace the first two registers, but builds directly on their logic — and comes with its own, clear disclaimer: only a rough first recommendation, no substitute for a well-considered, model-specific choice.

And afterwards?

Every distribution family in Register 2 links directly into Prior Lab, with a matching pre-selected distribution, link function, and intercept/slope view — there you then fine-tune the concrete parameters interactively and see live what your prior means on the response scale (including prior predictive simulation). Prior Compass gives you the starting point and the way of thinking, Prior Lab the tool for further exploration — the two tools are deliberately designed as a pair, not as a substitute for one another.

A simple linear equation, written as a distributional statement: Y ~ Normal(β₀ + β₁·X₁ + β₂·X₂, σ) — X₁ is metric, X₂ is binary (0/1). Every prediction is therefore not exact, but normally distributed around β₀+β₁·X₁+β₂·X₂ with spread σ. Pick an outcome variable (DV), then click a term to see what it controls and what range of values is plausible for its prior. σ, too, is a parameter that absolutely needs a prior — just like β₀, β₁ and β₂.

Click β₀, β₁·X₁, β₂·X₂ or σ

Priors in brms are specified on the model scale (η, linear predictor) — not on the scale on which you actually observe the data (probability, rate, mean). For Gaussian these are the same scale; for the other three families a link function sits in between, which is anything but linear. Choose a family:

⚠ Important note before you start

This wizard gives — purely as an example, guided by simple general principles and the ±2×SD thumb rule — a first, rough orientation. It does not replace the careful, model-specific choice of your priors. The concrete parametrization for your model always needs to be well thought through. Use the recommendation below only as a starting point, and then make sure to check it yourself: explore the distribution thoroughly in Prior Lab, and run a real prior predictive check in Bayesian PP Check for your concrete model, to see whether your prior actually produces plausible predictions. Don't blindly rely on thumb rules or default settings.

Answer three short questions — what type of outcome, which parameter, what plausible range of values — and the wizard suggests a prior distribution with a deep link into Prior Lab.