Beta prior from mean and uncertainty
Translate a probability mean and SD into compatible beta prior shapes.
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Enter probabilities on the 0–1 scale. The mean must be strictly between zero and one; SD must be positive and below sqrt(mean × (1−mean)).
The starting values are hypothetical. Results update as you edit. Use aggregate or synthetic inputs only.
Calculation results
- Alpha
- 6
- Beta
- 14
- Concentration
- 20
- Shape warning
- Both shapes are at least one.
How to interpret the output
Moment matching gives concentration mean×(1−mean)/variance−1. Shapes below one imply boundary-peaked densities, which may differ from an intended central prior. Prior concentration is a shape total, not an actual number of observed participants. Inspect sensitivity to several plausible priors.
Method referenceSource checked 2026-11-06. Read the reproducible calculator validation report.