Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the general bayes’ theorem calculator works
P(Hᵢ|E)=P(Hᵢ)P(E|Hᵢ)/ΣⱼP(Hⱼ)P(E|Hⱼ).
A posterior redistributes probability among the entered exhaustive hypotheses; it remains conditional on the chosen priors and likelihood model.
Worked example
General Bayes’ Theorem example
Priors 0.4 and 0.6 with likelihoods 0.2 and 0.5 produce posteriors about 0.2105 and 0.7895 after the evidence.
P(Hᵢ|E)=P(Hᵢ)P(E|Hᵢ)/ΣⱼP(Hⱼ)P(E|Hⱼ).
Supported inputs
Precision and limits
Model and design
Priors must total one, lists must align, hypotheses must be mutually exclusive and exhaustive, and the evidence probability must be positive.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
A posterior redistributes probability among the entered exhaustive hypotheses; it remains conditional on the chosen priors and likelihood model.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
Continue calculating