.. _sphx_glr_api_gallery_probability_mcmc:

Markov chain Monte Carlo
--------------------------

The Metropolis-Hastings algorithm and the Gibbs sampler.


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    <div class="sphx-glr-thumbcontainer" tooltip="Hastings (1970) generalized the 1953 Metropolis algorithm into a recipe for sampling any density \pi known only up to a constant: propose y \sim q(\cdot \mid x), accept with probability \min\bigl(1, \pi(y)q(x \mid y) / \pi(x)q(y \mid x)\bigr). Geman and Geman (1984) sampled images one pixel at a time from its conditional distribution given the rest: the Gibbs sampler.">

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  .. image:: /api/gallery/probability/mcmc/images/thumb/sphx_glr_plot_01_metropolis_hastings_gibbs_thumb.png
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  :doc:`/api/gallery/probability/mcmc/plot_01_metropolis_hastings_gibbs`

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      <div class="sphx-glr-thumbnail-title">Markov chain Monte Carlo: Metropolis-Hastings and the Gibbs sampler</div>
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    </div>


.. toctree::
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   /api/gallery/probability/mcmc/plot_01_metropolis_hastings_gibbs