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Statistics · Probability

General Bayes’ Theorem Calculator

Update several mutually exclusive hypotheses from their priors and the likelihood of the same observed evidence under each hypothesis.

Statistics · Probability

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Private in-browser calculation · explicit assumptions
Follow each branch by multiplying conditional probabilities; add mutually exclusive terminal paths when the question combines them.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

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Understand the probability

What the general bayes’ theorem calculator is calculating

Following conditional branches. Conditional probability changes the reference group. A branch probability must be read inside the branch condition, while Bayes’ theorem reverses the conditioning direction using prior probabilities.

Probability rule

P(Hᵢ|E)=P(Hᵢ)P(E|Hᵢ)/ΣⱼP(Hⱼ)P(E|Hⱼ).

Every probability must remain between 0 and 1, and overlapping regions must be jointly feasible. The calculator rejects combinations that violate the stated model.

How to interpret it

A posterior redistributes probability among the entered exhaustive hypotheses; it remains conditional on the chosen priors and likelihood model.

Model boundary: Priors must total one, lists must align, hypotheses must be mutually exclusive and exhaustive, and the evidence probability must be positive.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. 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.

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