Posterior Beta
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Posterior Beta calculator updates a Beta distribution with new data in a Bayesian framework. The posterior formula is Beta(α + h, β + m − h), where α and β are prior parameters, h is successes, and m is total trials. This is common for binomial experiments like clinical trials or approval surveys.
To use it, input the prior parameters (α, β), observed successes (h), and total trials (m). The posterior reflects updated knowledge by combining prior and new evidence. The Beta distribution models probabilities between 0 and 1 effectively.
It applies when data follows a binomial distribution. For example, modeling website conversion rates or test accuracy. Caution: ensure independent trials and constant probability. Adjust if dependencies exist.
Avoid small samples where the prior overpowers results. Confirm data fits defined successes/ failures. Ideal for iterative studies where new info refines predictions.
Frequently asked questions
What parameters do I need?
Provide prior parameters (α, β), observed successes (h), and total trials (m).
Why use this calculator?
It updates statistical beliefs with new data, ideal for binomial experiments like A/B tests or clinical trials.
How to interpret the result?
The posterior Beta shows updated probabilities after incorporating new data, with adjusted α and β.
When not to use it?
For non-binomial data (e.g., Poisson counts) or dependent events, use another model.
Practical example?
Testing a new drug: 50 successes in 100 trials update prior Beta(2,2) to Beta(52,52).