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Bayesian Inference

How should evidence change your mind? Bayesian inference combines a prior belief with observed data to produce a sharper posterior — watch it update in real time.

Bayesian InferenceLive

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Bayesian inference updates a prior belief with data to form a posterior. For a coin, a Beta prior combined with binomial coin flips gives a Beta posterior — the conjugate update is just adding heads to α and tails to β. Watch the posterior sharpen and shift as evidence accumulates.

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Data Inspector

Posterior mean0.667
Posterior SD0.094
Posterior α, β16.0, 8.0

Governing equation

Reading this result: The posterior mean 0.667 sits between the prior mean 0.500 and the observed rate 0.700; with 20 flips versus 4.0 pseudo-counts, the data dominates and pulls the estimate toward the evidence.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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How it works

Bayes' theorem multiplies a prior distribution by the likelihood of the data to get the posterior. For a coin's bias, a Beta prior and binomial data combine into a Beta posterior via a simple conjugate update: add heads to α and tails to β. As data accumulates, the posterior narrows and overrides the prior.

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Frequently asked questions

Is this Bayesian inference simulator tool really free?
Yes. Bayesian Inference runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.