Calculation Result
Formula used
Interpretation
Calculation steps
| Hypothesis or class | Prior | Likelihood | Unnormalised score | Posterior |
|---|
Merged calculation summary
Calculator Inputs
Choose a Bayesian calculation mode. Enter probabilities as decimals, percentages, fractions, odds, or scientific notation where supported.
How to Use
Select the calculation mode matching your problem. Enter each prior and evidence likelihood carefully. Press calculate to view normalised posterior probabilities.
Use percentages, fractions, decimals, or scientific notation. Multi-class and log modes accept any number of classes. Export the completed analysis when needed.
Review warnings before trusting unusual results. Compare priors against posteriors in the chart. Strong evidence should move probability in sensible directions.
Example Data
| Example | Prior | Likelihood | Evidence or competing likelihood | Expected use |
|---|---|---|---|---|
| Spam filtering | 0.30 | 0.85 | 0.15 | Binary classification |
| Medical screening | 0.10 | 0.90 sensitivity | 0.95 specificity | Diagnostic test |
| Three image classes | 0.50, 0.30, 0.20 | 0.70, 0.40, 0.10 | Normalised automatically | Multi-class model |
| Odds update | 0.20 | LR = 4 | Posterior odds = prior odds × LR | Evidence strength |
Calculation History
Recent calculations are stored locally in this browser.
Frequently Asked Questions
What is posterior probability?
Posterior probability is an updated belief after observing evidence. It combines a prior belief with an evidence likelihood. Bayes theorem performs the update mathematically.
What is a prior probability?
A prior describes belief before new evidence appears. It may come from historical data or domain knowledge. Priors should be justified and documented clearly.
What is likelihood?
Likelihood measures how probable evidence is under a hypothesis. It is not automatically the hypothesis probability. Confusing both values creates incorrect conclusions.
Why are multi-class results normalised?
Raw Bayesian scores rarely sum to one. Normalisation converts scores into comparable class probabilities. The resulting posterior values sum to one.
Can I enter percentages?
Yes, values such as 25% are accepted. Fractions like 1/4 also work. Scientific notation remains available for tiny probabilities.
What is a Bayes factor?
A Bayes factor compares evidence support between hypotheses. Values above one favour the first hypothesis. Values below one favour its alternative.
Why use log probabilities?
Very small probabilities may underflow during multiplication. Log probabilities replace multiplication with addition. Log-sum-exp then produces stable normalised results.
What causes impossible evidence warnings?
Impossible evidence has zero total probability under every class. Bayes theorem cannot divide by zero. Review likelihoods and class definitions carefully.
Does a high posterior prove a class?
No probability alone proves a hypothesis absolutely. Results depend on priors, likelihoods, and model assumptions. Validate the model using reliable held-out data.