Prior Probability Calculator

Calculator

Method

Choose how you want to create the prior.

Outcome A count (a)

Examples: successes, positives, or occurrences.

Outcome B count (b)

Examples: failures, negatives, or non-occurrences.

After calculating, use the buttons in the results card to download.

Example Data Table

Scenario	Input Type	Sample Inputs	Prior Output
Coin bias assumption	Binary counts	A=60, B=40	P(A)=0.60, P(B)=0.40
Three hypotheses	Multiclass counts	H1=25, H2=50, H3=25	0.25, 0.50, 0.25
Expert weighting	Normalize weights	0.2, 0.5, 0.3	0.20, 0.50, 0.30

Formula Used

A prior probability distributes belief across outcomes before new evidence.

Binary from counts: P(A)=a/(a+b) and P(B)=b/(a+b).
Multiclass from counts: P(H_i)=c_i / Σc.
Normalize weights: P(H_i)=w_i / Σw (for nonnegative weights).

How to Use This Calculator

Select a method that matches your available information.
Enter counts or weights for each outcome or hypothesis.
Press Submit to compute the prior distribution.
Review totals and the highest-prior hypothesis shown.
Use Download CSV or Download PDF for records.

FAQs

1) What is a prior probability?

A prior probability is an initial belief about outcomes before observing new data. It helps you start reasoning consistently, especially in Bayesian updates and model comparisons.

2) When should I use counts instead of weights?

Use counts when you have historical frequencies or observations. Use weights when evidence is subjective, expert-driven, or only relative strength is known.

3) What if my weights already sum to one?

The calculator still normalizes them. If they sum to one, the normalized results remain unchanged, aside from small rounding differences in the display.

4) Can priors be zero?

Yes, but a zero prior means you fully rule out that hypothesis. In Bayesian work, that hypothesis cannot recover later, even with strong evidence.

5) Why must inputs be nonnegative?

Counts and weights represent magnitude or support. Negative values do not fit probability construction and can create invalid totals or misleading priors.

6) How do I interpret the “largest prior” line?

It points to the outcome with the highest starting belief. It is not a final decision, but it shows which hypothesis dominates before new evidence is applied.

7) Does this replace Bayesian updating?

No. This tool builds the starting distribution. To update with evidence, combine priors with likelihoods and renormalize to form posterior probabilities.