Prior Predictive Simulation

Linear Regression — What Does Your Prior Imply About Data?

Drag σ_β to change the prior on the slope. Each draw samples α ~ N(0, 10²) and β ~ N(0, σ_β²), then plots E[y|x] = α + βx. Watch "vague" priors generate implausible near-vertical lines.

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Prior Predictive Lines — E[y | x]

Prior on Slope β

Slope Prior σ_β = σ of β ~ N(0, σ²)

0.1 1.0 6.0

Number of Prior Draws

20 150 400

Random Seed

1 42 99

Prior Preset

Prior Specification

Intercept Prior

α ~ N(0, 10²)

Slope Prior

β ~ N(0, 1²)

Model

E[y|x] = α + βx

Predictor Range

x ∈ [−2, 2]

n Lines Drawn

150

y-axis Clipped To

± ∞

—

|β| > 10 in prior

—

|β| > 50 in prior

—

Mean |Δy| over x

—

SD of drawn β

—

Prior assessment