.. _sphx_glr_api_gallery_probability_bayes:

Bayesian inference
-------------------

Bayes's Beta-binomial update and Laplace's rule of succession.


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    <div class="sphx-glr-thumbcontainer" tooltip="Starting from Bayes&#x27;s uniform prior, the posterior for an unknown success probability p after k successes in n trials is \mathrm{Beta}(k+1, n-k+1). It narrows around the true value as data accumulate, and its mean is Laplace&#x27;s rule of succession (k+1)/(n+2).">

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  :doc:`/api/gallery/probability/bayes/plot_01_bayes_rule_of_succession`

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      <div class="sphx-glr-thumbnail-title">Bayes's problem: learning a probability from data</div>
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.. toctree::
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   /api/gallery/probability/bayes/plot_01_bayes_rule_of_succession