From: Wolfgang Bangerth <bangerth@colostate.edu>
Date: Thu, 16 Jan 2020 21:22:13 +0000 (-0700)
Subject: Augment documentation.
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=1067e932e34c60bdd52d36b217b2f7eb952954b6;p=code-gallery.git

Augment documentation.
---

diff --git a/MCMC-Laplace/mcmc-laplace.cc b/MCMC-Laplace/mcmc-laplace.cc
index 47417a0..483ea24 100644
--- a/MCMC-Laplace/mcmc-laplace.cc
+++ b/MCMC-Laplace/mcmc-laplace.cc
@@ -571,7 +571,7 @@ namespace ProposalGenerator
 // The last main class is the Metropolis-Hastings sampler itself.
 // If you understand the algorithm behind this method, then
 // the following implementation should not be too difficult
-// to understand. The only thing of relevance is that descriptions
+// to read. The only thing of relevance is that descriptions
 // of the algorithm typically ask whether the *ratio* of two
 // probabilities (the "posterior" probabilities of the current
 // and the previous samples, where the "posterior" is the product of the
@@ -580,7 +580,12 @@ namespace ProposalGenerator
 // *logarithms* of these probabilities, we now need to take
 // the ratio of appropriate exponentials -- which is made numerically
 // more stable by considering the exponential of the difference of
-// the log probabilities.
+// the log probabilities. The only other slight complication is that
+// we need to multiply this ratio by the ratio of proposal probabilities
+// since we use a non-symmetric proposal distribution. This makes the
+// formula for accepting a sample slightly more awkward, but if you
+// take exponentials on both sides of the comparison, the formula
+// should become obvious again.
 namespace Sampler
 {
   class MetropolisHastings