How it works
Beta prior parameters and binomial successes give posterior mean (successes+alpha)/(trials+alpha+beta). This form solves for posterior mean proportion; enter the known quantities in Success count, Trial count, Prior alpha parameter, Prior beta parameter.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Success count | 4 | Formula symbol: successes. Enter a numeric value. Use a whole number. Use a non-negative value. |
| Trial count | 8 | Formula symbol: trials. Enter a numeric value. Use a whole number. Use a non-negative value. |
| Prior alpha parameter | 1 | Formula symbol: alpha. Enter a numeric value. Must be greater than zero. |
| Prior beta parameter | 1 | Formula symbol: beta. Enter a numeric value. Must be greater than zero. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Success count
- 4
- Trial count
- 8
- Prior alpha parameter
- 1
- Prior beta parameter
- 1
Complete example results
- Posterior mean proportion
- 50 %
Reading the result
The result solves for posterior mean proportion from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the posterior mean proportion result?
Independent Bernoulli observations and a chosen beta prior are assumed. Target successes round up; this is neither a probability guarantee nor an interval. Prior parameters must be positive.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: ocw.mit.edu