Beta–binomial evidence update
Update a stated beta prior with independent binary counts and inspect a credible interval.
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Use prior shape parameters of at least 0.1 and whole counts; successes cannot exceed trials. Shapes plus counts are capped at 10,000 for this numerical implementation.
The starting values are hypothetical. Results update as you edit. Use aggregate or synthetic inputs only.
Calculation results
- Posterior alpha
- 10
- Posterior beta
- 4
- Posterior mean
- 0.71428571
- 95% credible lower
- 0.46186846
- 95% credible upper
- 0.90907961
How to interpret the output
The posterior is Beta(alpha+successes,beta+failures). The equal-tailed 95% credible interval is conditional on the stated prior and exchangeable independent Bernoulli observations. It is not a frequentist confidence interval or proof of efficacy.
Method referenceSource checked 2026-11-06. Read the reproducible calculator validation report.