From eb2803bc987b91688de6731c9edb325ecaa8d11d Mon Sep 17 00:00:00 2001
From: Hu Zhao <zhao@mbd.rwth-aachen.de>
Date: Sat, 15 Apr 2023 17:59:35 +0200
Subject: [PATCH] docs: add description of metropolis hastings sampling

---
 docs/source/sampler/metropolis_hastings.rst | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/docs/source/sampler/metropolis_hastings.rst b/docs/source/sampler/metropolis_hastings.rst
index 6b2c868..cedb0b5 100644
--- a/docs/source/sampler/metropolis_hastings.rst
+++ b/docs/source/sampler/metropolis_hastings.rst
@@ -1,6 +1,27 @@
 Metropolis Hastings Sampling
 ============================
 
+Metropolis Hastings sampling is a widely used Markov Chain Monte Carlo (MCMC)
+algorithm for generating a sequence of samples from a target probability
+distribution where direct sampling is difficult. The samples can be used to
+estimate properties of the target distribution, like its mean, variance, and higher
+moments. The samples can also be used to approximate the target distribution,
+for example via a histogram. The algorithm works by constructing a Markov chain
+with a stationary distribution equal to the target distribution. 
+
+Steps of the algorithm are as follows:
+
+  1. Choose an initial state for the Markov chain, usually from the target distribution.
+  2. At each iteration, propose a new state by sampling from a proposal distribution.
+  3. Calculate the acceptance probability.
+  4. Accept or reject the proposed state based on the acceptance probability.
+  5. Repeat steps 2-4 for a large number of iterations to obtain a sequence of samples.
+  6. Apply "burn-in" and "thining".
+
+Final samples from the Markov chain can then be used to estimate the target
+distribution or its properties.
+       
+
 MetropolisHastings Class
 ------------------------
 
-- 
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