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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.pylink.pylink.within_range.html b/docs/build/html/_autosummary/bayesvalidrox.pylink.pylink.within_range.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.pylink.pylink.within_range.html
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
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 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index 88166ae557a8ac4d2c5b58049ce6421b53f6da77..00c0b14a84a9171d1c90a97cdd954d78ba3e9e8e 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.adaptPlot.adaptPlot.html
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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index dc183669e991009b0b317be369c56cfe4877392b..31ded85657492467d4814ceb77105ab9b3312ec9 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.adaptPlot.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.adaptPlot.html
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index 7fd894a2b05c2238263ca95d94ebe67ef701af04..cfa68525972b7938053f68e8eae4374aa9512cf5 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.apoly_construction.apoly_construction.html
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@@ -170,7 +170,8 @@
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.apoly_construction.html
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.BayesianLinearRegression.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.BayesianLinearRegression.html
index e3f16fb5c421af8aef20e6ad48e17acc12af2cc3..3dee9c9805fcccaebe781d3dad6c9c7e255a8d92 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.BayesianLinearRegression.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.BayesianLinearRegression.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.EBLinearRegression.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.EBLinearRegression.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.EBLinearRegression.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.EBLinearRegression.html
@@ -170,7 +170,8 @@
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.VBLinearRegression.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.VBLinearRegression.html
index 3ba8a66cb906826dceb78ad5e49f2025a5b042d7..49002d5f3ad44f76b604b9d87b280bf30604a146 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.VBLinearRegression.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.VBLinearRegression.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.gamma_mean.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.gamma_mean.html
index c3b2d56673133ba59dd38d065605a6d4e5a67186..f9446b9c30f385ca4ad6c1f66cfc05a3d9ed1c98 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.gamma_mean.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.gamma_mean.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.html
@@ -170,7 +170,8 @@
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
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 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.Engine.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.Engine.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.Engine.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.Engine.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.hellinger_distance.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.hellinger_distance.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.logpdf.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.logpdf.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.logpdf.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.logpdf.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.subdomain.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.subdomain.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.subdomain.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.subdomain.html
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule.html
@@ -170,7 +170,8 @@
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index dde4517e0c995b2c29d94649c97c2c919b3a589a..936d75c876a538186eb06d729c8db840b4f48e51 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule_arbitrary.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule_arbitrary.html
@@ -170,7 +170,8 @@
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index cc0f1d31cfbdd9bffc41e1755edfb2958379dde0..8a43256783ed04f6ab6d2c136c868a6a08473aa6 100644
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+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_univ_basis.html
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index 58709347de4066cf52315788d2b403067aed34e2..e566e9fc99989237f175a8313b24f228f845c8fa 100644
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index b13d05c48d065df1dcaea836b0d1ca9fcbdf9064..211d11ec9cebbbe03da83cb0cd51b11b0f2b0da2 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.poly_rec_coeffs.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.poly_rec_coeffs.html
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index 6548c9a3976e781288bcb9afb7f18c13f91d17bb..ebb205a5b7b266e9b1a0e311ec1acc8bf57d44ba 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.ExpDesigns.html
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@@ -170,7 +170,8 @@
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index c9556e4315c0343672ac2692d4c7b940a44de4d1..3f8c99c60c8dd63fa9a94a927f2e293699489f0a 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.check_ranges.html
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index 0a54834e033be55f36faa4bf9341ac15ce40fdf6..12f3e3b7b66a1370b00dc69415423fa565ed9b25 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.html
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index 4496b2d8f717108f8ae3821169740ccaeae2cbd7..bfc9e488793e12d2fb6ad190a3e9f763fcc99218 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.Exploration.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.Exploration.html
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index 5482569e1e7bd5a8e74fc2b8952952af366bd1d5..4fe52523a59bd299d130c541151d1ab08ee914c0 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.html
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.cross_truncate.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.cross_truncate.html
index 5a03208c86819cc3e68adf1b35a9d5ac9c0ce90b..ef1e59d9f481edf25afe4cb78d250a75f1836ec9 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.cross_truncate.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.cross_truncate.html
@@ -170,7 +170,8 @@
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index a950df2ff0a2fc8f4c0aa58deb6e0e70982e5e70..128c4263055ecdbbcc5d460d2d56ea0d769d1c16 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.glexindex.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.glexindex.html
@@ -170,7 +170,8 @@
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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index 96400f3335ee9fefce7b8c74b73b5d7b6540132d..f22f1237773177ce5762b38a38886c265b3ef192 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.html
@@ -170,7 +170,8 @@
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.input_space.InputSpace.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.input_space.InputSpace.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.input_space.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.input_space.html
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.Input.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.Input.html
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+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.Marginal.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.Marginal.html
@@ -170,7 +170,8 @@
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-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
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 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.html
index d5c3b12c17f42351a7d5ce1b97793db0d014d893..4e16820e398f7ce11159e57c7b6a96aaf03160b5 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.OrthogonalMatchingPursuit.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.OrthogonalMatchingPursuit.html
index 43f20bf429b54517e920f5cc4caad9ba94e71352..7e9829327c67c5f597d11b613427c8ff235d4705 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.OrthogonalMatchingPursuit.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.OrthogonalMatchingPursuit.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.corr.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.corr.html
index 274d8319d15ce6f02bb11570b0f04de5d05ec170..8f61f3d066b8c15efb6f1dc676309ef43da0101c 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.corr.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.corr.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.html
index f159c07b7d16bbea3883c98dccd211d0ce7e19a3..17f469e71810fd245e0abc4031a8ef2cbf00ced4 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.RegressionFastARD.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.RegressionFastARD.html
index 35ea14b81f33c21e5170f9ac5952fb87f1d38449..9dd1a74ff43fc63ee450278fb426515e5227df45 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.RegressionFastARD.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.RegressionFastARD.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.html
index f1a15392db7b92fd33289c6a80f192bf29ad688c..dcd0820e6d30a0bce8985938c8f7ad84dc0fbcf5 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.update_precisions.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.update_precisions.html
index ff1c030d120352eb3d7e6361764305295eb5ea81..05bcfb125d1a1b213e0db08d458290d7fef80fa1 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.update_precisions.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.update_precisions.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.RegressionFastLaplace.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.RegressionFastLaplace.html
index dc6b45be7b458da14c03fc147d90f0fc698b1eab..5ea393418ba57aac457d61fe83b4c22a18a98cb5 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.RegressionFastLaplace.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.RegressionFastLaplace.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.html
index 39bed6efb714b788a749f3800f756d641d8ab6d8..8ed5c18d58d878e5b16fcba867f0941b39449dff 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.MetaModel.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.MetaModel.html
index 07bf13ba0b8fa37029609e50352dc6c58416f484..b19b796849a7a1500e42151901841e84e4dec613 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.MetaModel.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.MetaModel.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.corr_loocv_error.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.corr_loocv_error.html
index a047d2ad8298fa5a806499059658a45f4082a040..85883cb847cf1c65e2311dbcf9b1767ee88fd7f9 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.corr_loocv_error.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.corr_loocv_error.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.create_psi.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.create_psi.html
index 1b72a962cb784fc83d165f7b78c1ff34f2012271..4a66eb692ad6d7454d221ba2957f44131c9a5fe9 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.create_psi.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.create_psi.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.gaussian_process_emulator.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.gaussian_process_emulator.html
index 560f6c733c28d248e12526abe547a64accb91e9f..a38aa4e631828e0e30210cc27184f01c7b6072f1 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.gaussian_process_emulator.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.gaussian_process_emulator.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.html
index 82a65402e9c73ede08a4a8f24ca6a8bc459dbb98..bb5eaba6c656f8899f104b1832777061be31f5ed 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.surrogate_models.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/_sources/bayes_description.rst.txt b/docs/build/html/_sources/bayes_description.rst.txt
index 0406162ed8a5927c2f3aa1944142584820c20d75..0cb36d10f808a92e14d29abc01b9a7fd6883466b 100644
--- a/docs/build/html/_sources/bayes_description.rst.txt
+++ b/docs/build/html/_sources/bayes_description.rst.txt
@@ -56,7 +56,66 @@ The ``parameters`` contain the variance for each point in the observation.
 Now we can initialize an object of class :any:`bayesvalidrox.bayes_inference.bayes_inference.BayesInference` with all the wanted properties.
 This object has to be given our ``Engine``.
 If it should use the surrogate during inference, set ``emulator`` to ``True``, otherwise the model will be evaluated directly.
+We also set the defined ``Discrepancy``. and set ``post_plot_pred`` if posterior predictions should be visualized.
 
 >>> BayesObj = BayesInference(Engine_)
 >>> BayesObj.emulator = True
+>>> BayesObj.Discrepancy = DiscrepancyOpts
+>>> BayesObj.plot_post_pred = True
 
+In order to run with rejection sampling, we set the ``inference_method`` accordingly and add properties for ``bootstrap``.
+
+>>> BayesObj.inference_method = 'rejection'
+>>> BayesObj.bootstrap = True
+>>> BayesObj.n_bootstrap_itrs = 500
+>>> BayesObj.bootstrap_noise = 2
+
+If the sampling should be done with MCMC, then this is set as the ``inference_method`` and additional properties are given in ``mcmc_params``.
+For this example we use the python package ``emcee`` to define the MCMC moves.
+
+>>> BayesObj.inference_method = 'MCMC'
+>>> import emcee
+>>> BayesObj.mcmc_params = {
+>>>     'n_steps': 1e4,#5,
+>>>     'n_walkers': 30,
+>>>     'moves': emcee.moves.KDEMove(),
+>>>     'multiprocessing': False,
+>>>     'verbose': False
+>>>     }
+
+Then we run the inference.
+
+>>> BayesObj.create_inference()
+
+If the output directory ``BayesObj.out_dir`` is not set otherwise, the outputs are written into the folder ``Outputs_Bayes_model_Calib``.
+This folder includes the posterior distribution of the input parameters, as well as the predictions resulting from the mean of the posterior.
+For inference with MCMC, chain diagnostics are also written out in the console.
+
+.. container:: twocol
+
+   .. container:: leftside
+   
+      .. code-block:: py
+
+         ---------------Posterior diagnostics---------------
+         Mean auto-correlation time: 2.057
+         Thin: 1
+         Burn-in: 4
+         Flat chain shape: (13380, 1)
+         Mean acceptance fraction*: 0.752
+         Gelman-Rubin Test**:  [1.001]
+
+         * This value must lay between 0.234 and 0.5.
+         ** These values must be smaller than 1.1.
+         --------------------------------------------------
+		 
+   .. container:: rightside
+
+      .. image:: ../../examples/user_guide/Outputs_Bayes_model_Calib/Posterior_Dist_model_emulator.pdf
+         :width: 400
+         :alt: Posterior distribution of the input parameter
+		 
+      .. image:: ../../examples/user_guide/Outputs_Bayes_model_Calib/Post_Prior_Perd_model_emulator_A.pdf
+         :width: 400
+         :alt: Comparison of posterior prediction to the observation
+		 
\ No newline at end of file
diff --git a/docs/build/html/_sources/bmc_description.rst.txt b/docs/build/html/_sources/bmc_description.rst.txt
index 10e73bd1e819ad67df4fe48247a2bcf26fe698a7..b3eaf86c2ca702ffa9781de4f6f3224f87c479fb 100644
--- a/docs/build/html/_sources/bmc_description.rst.txt
+++ b/docs/build/html/_sources/bmc_description.rst.txt
@@ -1,7 +1,22 @@
 Bayesian multi-model comparison
 *******************************
+.. container:: twocol
 
-.. image:: ../diagrams/bayesian_model_comparison.png
-   :width: 400
-   :alt: UML diagram for classes related to Bayesian multi-model comparison.
+   .. container:: leftside
+   
+      Bayesvalidrox provides three distinct methods to compare sets of models against each other given some observation of the outputs, Bayes' Factors, model weights and confusion matrices.
+      These are contained within the class :any:`bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison` and can be called one-at-a-time with their respective functions, or consecutively with the function ``model_comparison_all()``.
+	  
+      
+   .. container:: rightside
+   
+      .. image:: ../diagrams/bayesian_model_comparison.png
+         :width: 400
+         :alt: UML diagram for classes related to Bayesian multi-model comparison.
 
+
+Example
+=======
+To perform model comparison, we first need to define the set of competing models.
+For this, we create two additional models based on the example model from :any:`model_description`.
+The first of these models 
\ No newline at end of file
diff --git a/docs/build/html/al_description.html b/docs/build/html/al_description.html
index 78a5f609efb6ef18b9a5cf743e0927f79504fb15..e3cde5ecdeba4d96aa5f5ae5687880f353b4cfdb 100644
--- a/docs/build/html/al_description.html
+++ b/docs/build/html/al_description.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2 current current-page"><a class="current reference internal" href="#">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/analyticalfunction.html b/docs/build/html/analyticalfunction.html
index 42509cf3862f35bffb524e96a08c1519f3cd6267..799f0350ab63fcff73326e688d496645156564eb 100644
--- a/docs/build/html/analyticalfunction.html
+++ b/docs/build/html/analyticalfunction.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/api.html b/docs/build/html/api.html
index d853aff4e2794fdef4103a72a3b981e1acafc568..7f918265aaa46ff4fce912683b613ad2fe00c692 100644
--- a/docs/build/html/api.html
+++ b/docs/build/html/api.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/bayes_description.html b/docs/build/html/bayes_description.html
index 4d5cfd6c6778cb15ccdb15917a9df9b2c78f98ca..487cb49bcb3232a3a6ff139ff4b954e25300bd07 100644
--- a/docs/build/html/bayes_description.html
+++ b/docs/build/html/bayes_description.html
@@ -389,11 +389,62 @@ The <code class="docutils literal notranslate"><span class="pre">parameters</spa
 </div>
 <p>Now we can initialize an object of class <a class="reference internal" href="_autosummary/bayesvalidrox.bayes_inference.bayes_inference.BayesInference.html#bayesvalidrox.bayes_inference.bayes_inference.BayesInference" title="bayesvalidrox.bayes_inference.bayes_inference.BayesInference"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.bayes_inference.bayes_inference.BayesInference</span></code></a> with all the wanted properties.
 This object has to be given our <code class="docutils literal notranslate"><span class="pre">Engine</span></code>.
-If it should use the surrogate during inference, set <code class="docutils literal notranslate"><span class="pre">emulator</span></code> to <code class="docutils literal notranslate"><span class="pre">True</span></code>, otherwise the model will be evaluated directly.</p>
+If it should use the surrogate during inference, set <code class="docutils literal notranslate"><span class="pre">emulator</span></code> to <code class="docutils literal notranslate"><span class="pre">True</span></code>, otherwise the model will be evaluated directly.
+We also set the defined <code class="docutils literal notranslate"><span class="pre">Discrepancy</span></code>. and set <code class="docutils literal notranslate"><span class="pre">post_plot_pred</span></code> if posterior predictions should be visualized.</p>
 <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span> <span class="o">=</span> <span class="n">BayesInference</span><span class="p">(</span><span class="n">Engine_</span><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">emulator</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">Discrepancy</span> <span class="o">=</span> <span class="n">DiscrepancyOpts</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">plot_post_pred</span> <span class="o">=</span> <span class="kc">True</span>
 </pre></div>
 </div>
+<p>In order to run with rejection sampling, we set the <code class="docutils literal notranslate"><span class="pre">inference_method</span></code> accordingly and add properties for <code class="docutils literal notranslate"><span class="pre">bootstrap</span></code>.</p>
+<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">inference_method</span> <span class="o">=</span> <span class="s1">&#39;rejection&#39;</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">bootstrap</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">n_bootstrap_itrs</span> <span class="o">=</span> <span class="mi">500</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">bootstrap_noise</span> <span class="o">=</span> <span class="mi">2</span>
+</pre></div>
+</div>
+<p>If the sampling should be done with MCMC, then this is set as the <code class="docutils literal notranslate"><span class="pre">inference_method</span></code> and additional properties are given in <code class="docutils literal notranslate"><span class="pre">mcmc_params</span></code>.
+For this example we use the python package <code class="docutils literal notranslate"><span class="pre">emcee</span></code> to define the MCMC moves.</p>
+<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">inference_method</span> <span class="o">=</span> <span class="s1">&#39;MCMC&#39;</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">emcee</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">mcmc_params</span> <span class="o">=</span> <span class="p">{</span>
+<span class="gp">&gt;&gt;&gt; </span>    <span class="s1">&#39;n_steps&#39;</span><span class="p">:</span> <span class="mf">1e4</span><span class="p">,</span><span class="c1">#5,</span>
+<span class="gp">&gt;&gt;&gt; </span>    <span class="s1">&#39;n_walkers&#39;</span><span class="p">:</span> <span class="mi">30</span><span class="p">,</span>
+<span class="gp">&gt;&gt;&gt; </span>    <span class="s1">&#39;moves&#39;</span><span class="p">:</span> <span class="n">emcee</span><span class="o">.</span><span class="n">moves</span><span class="o">.</span><span class="n">KDEMove</span><span class="p">(),</span>
+<span class="gp">&gt;&gt;&gt; </span>    <span class="s1">&#39;multiprocessing&#39;</span><span class="p">:</span> <span class="kc">False</span><span class="p">,</span>
+<span class="gp">&gt;&gt;&gt; </span>    <span class="s1">&#39;verbose&#39;</span><span class="p">:</span> <span class="kc">False</span>
+<span class="gp">&gt;&gt;&gt; </span>    <span class="p">}</span>
+</pre></div>
+</div>
+<p>Then we run the inference.</p>
+<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">BayesObj</span><span class="o">.</span><span class="n">create_inference</span><span class="p">()</span>
+</pre></div>
+</div>
+<p>If the output directory <code class="docutils literal notranslate"><span class="pre">BayesObj.out_dir</span></code> is not set otherwise, the outputs are written into the folder <code class="docutils literal notranslate"><span class="pre">Outputs_Bayes_model_Calib</span></code>.
+This folder includes the posterior distribution of the input parameters, as well as the predictions resulting from the mean of the posterior.
+For inference with MCMC, chain diagnostics are also written out in the console.</p>
+<div class="twocol docutils container">
+<div class="leftside docutils container">
+<div class="highlight-py notranslate"><div class="highlight"><pre><span></span><span class="o">---------------</span><span class="n">Posterior</span> <span class="n">diagnostics</span><span class="o">---------------</span>
+<span class="n">Mean</span> <span class="n">auto</span><span class="o">-</span><span class="n">correlation</span> <span class="n">time</span><span class="p">:</span> <span class="mf">2.057</span>
+<span class="n">Thin</span><span class="p">:</span> <span class="mi">1</span>
+<span class="n">Burn</span><span class="o">-</span><span class="ow">in</span><span class="p">:</span> <span class="mi">4</span>
+<span class="n">Flat</span> <span class="n">chain</span> <span class="n">shape</span><span class="p">:</span> <span class="p">(</span><span class="mi">13380</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="n">Mean</span> <span class="n">acceptance</span> <span class="n">fraction</span><span class="o">*</span><span class="p">:</span> <span class="mf">0.752</span>
+<span class="n">Gelman</span><span class="o">-</span><span class="n">Rubin</span> <span class="n">Test</span><span class="o">**</span><span class="p">:</span>  <span class="p">[</span><span class="mf">1.001</span><span class="p">]</span>
+
+<span class="o">*</span> <span class="n">This</span> <span class="n">value</span> <span class="n">must</span> <span class="n">lay</span> <span class="n">between</span> <span class="mf">0.234</span> <span class="ow">and</span> <span class="mf">0.5</span><span class="o">.</span>
+<span class="o">**</span> <span class="n">These</span> <span class="n">values</span> <span class="n">must</span> <span class="n">be</span> <span class="n">smaller</span> <span class="n">than</span> <span class="mf">1.1</span><span class="o">.</span>
+<span class="o">--------------------------------------------------</span>
+</pre></div>
+</div>
+</div>
+<div class="rightside docutils container">
+<a class="reference internal image-reference" href="_images/Posterior_Dist_model_emulator.pdf"><img alt="Posterior distribution of the input parameter" src="_images/Posterior_Dist_model_emulator.pdf" style="width: 400px;" /></a>
+<a class="reference internal image-reference" href="_images/Post_Prior_Perd_model_emulator_A.pdf"><img alt="Comparison of posterior prediction to the observation" src="_images/Post_Prior_Perd_model_emulator_A.pdf" style="width: 400px;" /></a>
+</div>
+</div>
 </section>
 </section>
 
diff --git a/docs/build/html/beam.html b/docs/build/html/beam.html
index 6c82f54b9c2f2bca66cd21adf154c9aa11a04319..64c4a4c02961b651df6c1cc9c11ae1648000a38b 100644
--- a/docs/build/html/beam.html
+++ b/docs/build/html/beam.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/bmc_description.html b/docs/build/html/bmc_description.html
index 03d4552b236f368fb27933296978b76f81b82ff7..15dc599433ada04bae09746e0b0a1d7444a92ea8 100644
--- a/docs/build/html/bmc_description.html
+++ b/docs/build/html/bmc_description.html
@@ -141,7 +141,7 @@
           <svg class="theme-icon-when-light"><use href="#svg-sun"></use></svg>
         </button>
       </div>
-      <label class="toc-overlay-icon toc-header-icon no-toc" for="__toc">
+      <label class="toc-overlay-icon toc-header-icon" for="__toc">
         <div class="visually-hidden">Toggle table of contents sidebar</div>
         <i class="icon"><svg><use href="#svg-toc"></use></svg></i>
       </label>
@@ -330,7 +330,7 @@
               <svg class="theme-icon-when-light"><use href="#svg-sun"></use></svg>
             </button>
           </div>
-          <label class="toc-overlay-icon toc-content-icon no-toc" for="__toc">
+          <label class="toc-overlay-icon toc-content-icon" for="__toc">
             <div class="visually-hidden">Toggle table of contents sidebar</div>
             <i class="icon"><svg><use href="#svg-toc"></use></svg></i>
           </label>
@@ -338,7 +338,21 @@
         <article role="main">
           <section id="bayesian-multi-model-comparison">
 <h1>Bayesian multi-model comparison<a class="headerlink" href="#bayesian-multi-model-comparison" title="Link to this heading">¶</a></h1>
+<div class="twocol docutils container">
+<div class="leftside docutils container">
+<p>Bayesvalidrox provides three distinct methods to compare sets of models against each other given some observation of the outputs, Bayes’ Factors, model weights and confusion matrices.
+These are contained within the class <a class="reference internal" href="_autosummary/bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison.html#bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison" title="bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison</span></code></a> and can be called one-at-a-time with their respective functions, or consecutively with the function <code class="docutils literal notranslate"><span class="pre">model_comparison_all()</span></code>.</p>
+</div>
+<div class="rightside docutils container">
 <a class="reference internal image-reference" href="_images/bayesian_model_comparison.png"><img alt="UML diagram for classes related to Bayesian multi-model comparison." src="_images/bayesian_model_comparison.png" style="width: 400px;" /></a>
+</div>
+</div>
+<section id="example">
+<h2>Example<a class="headerlink" href="#example" title="Link to this heading">¶</a></h2>
+<p>To perform model comparison, we first need to define the set of competing models.
+For this, we create two additional models based on the example model from <a class="reference internal" href="model_description.html"><span class="doc">Models</span></a>.
+The first of these models</p>
+</section>
 </section>
 
         </article>
@@ -384,9 +398,28 @@
         
       </footer>
     </div>
-    <aside class="toc-drawer no-toc">
+    <aside class="toc-drawer">
       
       
+      <div class="toc-sticky toc-scroll">
+        <div class="toc-title-container">
+          <span class="toc-title">
+            On this page
+          </span>
+        </div>
+        <div class="toc-tree-container">
+          <div class="toc-tree">
+            <ul>
+<li><a class="reference internal" href="#">Bayesian multi-model comparison</a><ul>
+<li><a class="reference internal" href="#example">Example</a></li>
+</ul>
+</li>
+</ul>
+
+          </div>
+        </div>
+      </div>
+      
       
     </aside>
   </div>
diff --git a/docs/build/html/borehole.html b/docs/build/html/borehole.html
index eafbe8618ff8d0757196ae0777a1cf723a5fffbe..683c27d0e04ec78a166d826a129aac151452cda5 100644
--- a/docs/build/html/borehole.html
+++ b/docs/build/html/borehole.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/examples.html b/docs/build/html/examples.html
index 9d6b6cce855166cfe6ef716ab177457dbfa207cc..4c621310a3263574de929c0bdd7f0468c73256fb 100644
--- a/docs/build/html/examples.html
+++ b/docs/build/html/examples.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/ishigami.html b/docs/build/html/ishigami.html
index 06d5b7d8c9adcb37841b53c2a5e31c6cdb19a142..dcf8bda0beb013af407cfc2bc09692aa9e5f66e9 100644
--- a/docs/build/html/ishigami.html
+++ b/docs/build/html/ishigami.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/modelcomparison.html b/docs/build/html/modelcomparison.html
index 723a66ed173227b1716a63d607f17305a2b44e17..472be01bb69119cbebd70a3d8d3d1a7eee0e5028 100644
--- a/docs/build/html/modelcomparison.html
+++ b/docs/build/html/modelcomparison.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/ohaganfunction.html b/docs/build/html/ohaganfunction.html
index cfe645ff03aebcd76205c1fc126f95d245425524..e7b7558755f9fd027a76475797e0e6836f331103 100644
--- a/docs/build/html/ohaganfunction.html
+++ b/docs/build/html/ohaganfunction.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
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index fec129dec57603707f017d18b9b872cf33c52b35..a142440bea3e1c65614a859aa3c0c7fd6477d370 100644
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\ No newline at end of file
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"witch": 44, "within": [10, 16, 69, 71], "without": [16, 64, 68, 70, 72, 74, 79, 82], "wolfgang": 29, "word": 16, "work": [16, 24, 25, 26, 52, 55, 70, 72, 74, 79, 82], "workflow": [72, 82], "wors": [24, 25, 26, 52, 55], "would": [24, 25, 26, 52, 55, 72], "wrapper": 16, "write": 9, "written": [16, 67], "wrong": 29, "www": [22, 33, 55, 58, 70, 74, 79], "x": [13, 16, 24, 25, 26, 31, 34, 35, 36, 39, 44, 47, 52, 53, 55, 58, 60, 63, 73, 75, 81, 82], "x1": 16, "x_1": [49, 50, 74, 82], "x_2": [74, 82], "x_3": 74, "x_axi": 13, "x_can": 29, "x_i": [44, 81], "x_mc": 29, "x_new": 29, "x_valu": [16, 20, 67, 72, 75, 81], "xi": 16, "xiu": 82, "xlabel": 13, "xnew": 29, "xx": 16, "xxa": 55, "xya": 55, "y": [7, 9, 24, 25, 26, 39, 52, 53, 55, 60, 61, 63], "y_hat": [25, 26, 29, 52, 55, 58], "y_i": 81, "y_pc_val": 20, "y_pc_val_std": 20, "y_pred": [24, 25, 26, 52, 55, 60], "y_true": [24, 25, 26, 52, 55], "y_val": 20, "ye": [16, 65, 68, 79], "yet": 10, "yew": 29, "you": [7, 13, 16, 24, 25, 26, 52, 55, 66, 70, 72, 74, 76, 77, 79], "young": 68, "your": [13, 70, 74, 77, 78], "yr": [70, 74], "z": [72, 82], "zero": [30, 52, 55, 58, 67], "zeromean": 7, "zip": 16, "zip_subdir": 16, "zurich": 33}, "titles": ["bayesvalidrox", "bayesvalidrox.bayes_inference", "bayesvalidrox.bayes_inference.bayes_inference", "bayesvalidrox.bayes_inference.bayes_inference.BayesInference", "bayesvalidrox.bayes_inference.bayes_model_comparison", "bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison", "bayesvalidrox.bayes_inference.discrepancy", "bayesvalidrox.bayes_inference.discrepancy.Discrepancy", "bayesvalidrox.bayes_inference.mcmc", "bayesvalidrox.bayes_inference.mcmc.MCMC", "bayesvalidrox.bayes_inference.mcmc.gelman_rubin", "bayesvalidrox.post_processing", "bayesvalidrox.post_processing.post_processing", "bayesvalidrox.post_processing.post_processing.PostProcessing", "bayesvalidrox.pylink", "bayesvalidrox.pylink.pylink", "bayesvalidrox.pylink.pylink.PyLinkForwardModel", "bayesvalidrox.pylink.pylink.within_range", "bayesvalidrox.surrogate_models", "bayesvalidrox.surrogate_models.adaptPlot", "bayesvalidrox.surrogate_models.adaptPlot.adaptPlot", "bayesvalidrox.surrogate_models.apoly_construction", "bayesvalidrox.surrogate_models.apoly_construction.apoly_construction", "bayesvalidrox.surrogate_models.bayes_linear", "bayesvalidrox.surrogate_models.bayes_linear.BayesianLinearRegression", "bayesvalidrox.surrogate_models.bayes_linear.EBLinearRegression", "bayesvalidrox.surrogate_models.bayes_linear.VBLinearRegression", "bayesvalidrox.surrogate_models.bayes_linear.gamma_mean", "bayesvalidrox.surrogate_models.engine", "bayesvalidrox.surrogate_models.engine.Engine", "bayesvalidrox.surrogate_models.engine.hellinger_distance", "bayesvalidrox.surrogate_models.engine.logpdf", "bayesvalidrox.surrogate_models.engine.subdomain", "bayesvalidrox.surrogate_models.eval_rec_rule", "bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule", "bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule_arbitrary", "bayesvalidrox.surrogate_models.eval_rec_rule.eval_univ_basis", "bayesvalidrox.surrogate_models.eval_rec_rule.poly_rec_coeffs", "bayesvalidrox.surrogate_models.exp_designs", "bayesvalidrox.surrogate_models.exp_designs.ExpDesigns", "bayesvalidrox.surrogate_models.exp_designs.check_ranges", "bayesvalidrox.surrogate_models.exploration", "bayesvalidrox.surrogate_models.exploration.Exploration", "bayesvalidrox.surrogate_models.glexindex", "bayesvalidrox.surrogate_models.glexindex.cross_truncate", "bayesvalidrox.surrogate_models.glexindex.glexindex", "bayesvalidrox.surrogate_models.input_space", "bayesvalidrox.surrogate_models.input_space.InputSpace", "bayesvalidrox.surrogate_models.inputs", "bayesvalidrox.surrogate_models.inputs.Input", "bayesvalidrox.surrogate_models.inputs.Marginal", "bayesvalidrox.surrogate_models.orthogonal_matching_pursuit", "bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.OrthogonalMatchingPursuit", "bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.corr", "bayesvalidrox.surrogate_models.reg_fast_ard", "bayesvalidrox.surrogate_models.reg_fast_ard.RegressionFastARD", "bayesvalidrox.surrogate_models.reg_fast_ard.update_precisions", "bayesvalidrox.surrogate_models.reg_fast_laplace", "bayesvalidrox.surrogate_models.reg_fast_laplace.RegressionFastLaplace", "bayesvalidrox.surrogate_models.surrogate_models", "bayesvalidrox.surrogate_models.surrogate_models.MetaModel", "bayesvalidrox.surrogate_models.surrogate_models.corr_loocv_error", "bayesvalidrox.surrogate_models.surrogate_models.create_psi", "bayesvalidrox.surrogate_models.surrogate_models.gaussian_process_emulator", "Active learning: iteratively expanding the training set", "Example: Analytical function", "API", "Bayesian inference", "Example: beam", "Bayesian multi-model comparison", "Example: borehole", "EXAMPLES", "Surrogate-assisted\u00a0Bayesian validation of computational models", "Priors, input space and experimental design", "Example: ishigami", "Models", "Example: model comparison", "Example: OHagan-function", "USER GUIDE", "Example: pollution", "Postprocessing", "Training surrogate models", "TUTORIAL"], "titleterms": {"1": 76, "3": 76, "activ": 64, "adaptplot": [19, 20], "also": [], "an": 82, "analyt": 65, "api": 66, "apoly_construct": [21, 22], "argument": [29, 42], "assist": 72, "attribut": [3, 5, 7, 9, 13, 16, 25, 26, 39, 42, 47, 49, 50, 52, 55, 58, 60], "bay": [], "bayes_infer": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], "bayes_linear": [23, 24, 25, 26, 27], "bayes_model_comparison": [4, 5], "bayesian": [67, 69, 72, 82], "bayesianlinearregress": 24, "bayesinfer": 3, "bayesmodelcomparison": 5, "bayesvalidrox": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63], "beam": 68, "borehol": 70, "check_rang": 40, "choic": [65, 68, 70, 74, 76, 77, 79], "class": [], "comparison": [69, 76], "comput": 72, "contact": [], "content": 72, "contribut": 72, "corr": 53, "corr_loocv_error": 61, "create_psi": 62, "cross_trunc": 44, "data": [65, 68, 70, 74, 77, 79, 82], "defin": 82, "descript": [], "design": [73, 82], "discrep": [6, 7, 65, 68], "eblinearregress": 25, "engin": [28, 29, 30, 31, 32, 81, 82], "eval_rec_rul": [33, 34, 35, 36, 37], "eval_rec_rule_arbitrari": 35, "eval_univ_basi": 36, "exampl": [49, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81], "exp_design": [38, 39, 40], "expand": 64, "expdesign": 39, "experiment": [73, 82], "exploit": 64, "explor": [41, 42, 64], "function": [65, 77], "further": 72, "gamma_mean": 27, "gaussian_process_emul": 63, "gelman_rubin": 10, "glexindex": [43, 44, 45], "guid": 78, "hellinger_dist": 30, "import": 82, "indic": 72, "infer": [67, 82], "input": [48, 49, 50, 73, 82], "input_spac": [46, 47], "inputspac": 47, "instal": [72, 78], "introductori": [], "ishigami": 74, "iter": 64, "l2_model": 76, "learn": 64, "librari": 82, "licens": 72, "link": 72, "logpdf": 31, "margin": 50, "mcmc": [8, 9, 10], "meta": 82, "meta_model_engin": [], "metamodel": [60, 65, 68, 70, 74, 76, 77, 79, 81], "model": [65, 68, 69, 70, 72, 74, 75, 76, 77, 79, 81, 82], "model1": 76, "multi": 69, "necessari": 82, "nl2_model": 76, "nl4_model": 76, "note": [24, 25, 26, 39, 52, 55, 60], "ohagan": 77, "option": 81, "orthogonal_matching_pursuit": [51, 52, 53], "orthogonalmatchingpursuit": 52, "overview": 78, "packag": [], "paramet": [3, 5, 7, 9, 10, 13, 16, 17, 22, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 47, 52, 55, 58, 60, 61, 62, 63], "pollut": 79, "poly_rec_coeff": 37, "post": 82, "post_process": [11, 12, 13], "postprocess": [13, 80], "prior": [65, 68, 70, 73, 74, 77, 79], "priors1": 76, "probabilist": 82, "process": 82, "pylink": [14, 15, 16, 17, 65, 68, 70, 74, 76, 77, 79], "pylinkforwardmodel": [16, 82], "quickstart": 72, "rais": [13, 29, 62], "refer": [52, 55, 58], "reg_fast_ard": [54, 55, 56], "reg_fast_laplac": [57, 58], "regressionfastard": 55, "regressionfastlaplac": 58, "return": [3, 5, 7, 9, 10, 13, 16, 17, 22, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 42, 47, 49, 52, 55, 58, 60, 61, 62, 63], "see": [], "sequenti": 82, "set": [64, 65, 68, 70, 74, 76, 77, 79, 82], "space": 73, "subdomain": 32, "surrog": [65, 68, 70, 72, 74, 76, 77, 79, 81, 82], "surrogate_model": [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63], "tabl": 72, "theori": [], "tradeoff": 64, "train": [64, 65, 68, 70, 74, 76, 77, 79, 81, 82], "tutori": 82, "uncertainti": 82, "update_precis": 56, "user": 78, "valid": 72, "vblinearregress": 26, "within_rang": 17}})
\ No newline at end of file
diff --git a/docs/build/html/surrogate_description.html b/docs/build/html/surrogate_description.html
index c48db82a4773b839e34ca20dce1c610bb97ffb3a..db4708ce672e7ec6bdb91614f5e36b2b7aabec9a 100644
--- a/docs/build/html/surrogate_description.html
+++ b/docs/build/html/surrogate_description.html
@@ -170,7 +170,8 @@
 <li class="toctree-l2 current current-page"><a class="current reference internal" href="#">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial.html">TUTORIAL</a></li>
diff --git a/docs/build/html/tutorial.html b/docs/build/html/tutorial.html
index 820f6d348870c77e961ce0e23f2158a2279322da..f4c9412913a544299343f5beb0e73c9ed9800d0d 100644
--- a/docs/build/html/tutorial.html
+++ b/docs/build/html/tutorial.html
@@ -3,7 +3,7 @@
   <head><meta charset="utf-8"/>
     <meta name="viewport" content="width=device-width,initial-scale=1"/>
     <meta name="color-scheme" content="light dark"><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
-<link rel="index" title="Index" href="genindex.html" /><link rel="search" title="Search" href="search.html" /><link rel="next" title="EXAMPLES" href="examples.html" /><link rel="prev" title="Bayesian inference and multi-model comparison" href="bayes_description.html" />
+<link rel="index" title="Index" href="genindex.html" /><link rel="search" title="Search" href="search.html" /><link rel="next" title="EXAMPLES" href="examples.html" /><link rel="prev" title="Bayesian multi-model comparison" href="bmc_description.html" />
 
     <!-- Generated with Sphinx 7.3.7 and Furo 2023.09.10 -->
         <title>TUTORIAL - bayesvalidrox 1.0.0 documentation</title>
@@ -170,7 +170,8 @@
 <li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li>
 <li class="toctree-l2"><a class="reference internal" href="al_description.html">Active learning: iteratively expanding the training set</a></li>
 <li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing</a></li>
-<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference and multi-model comparison</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bayes_description.html">Bayesian inference</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bmc_description.html">Bayesian multi-model comparison</a></li>
 </ul>
 </li>
 <li class="toctree-l1 current current-page"><a class="current reference internal" href="#">TUTORIAL</a></li>
@@ -596,7 +597,7 @@ The method <code class="docutils literal notranslate"><span class="pre">sobolInd
 </div>
 <p>If we set <code class="docutils literal notranslate"><span class="pre">emulator</span></code> to be true the Bayesian Inference will be performed based on the emulator.
 Some posterior predictions will be plotted by setting <code class="docutils literal notranslate"><span class="pre">plot_post_pred</span></code>.
-More options for Bayesian inference are listed at <a class="reference internal" href="bayes_description.html"><span class="doc">Bayesian inference and multi-model comparison</span></a>.</p>
+More options for Bayesian inference are listed at <a class="reference internal" href="bayes_description.html"><span class="doc">Bayesian inference</span></a>.</p>
 <div class="admonition note">
 <p class="admonition-title">Note</p>
 <p>Setting <code class="docutils literal notranslate"><span class="pre">emulator</span> <span class="pre">=</span> <span class="pre">False</span></code> means that the inference is based on actual model runs and not the surrogate.
@@ -694,14 +695,14 @@ plots of posterior predictions if wanted.</p>
               </div>
               <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg>
             </a>
-          <a class="prev-page" href="bayes_description.html">
+          <a class="prev-page" href="bmc_description.html">
               <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg>
               <div class="page-info">
                 <div class="context">
                   <span>Previous</span>
                 </div>
                 
-                <div class="title">Bayesian inference and multi-model comparison</div>
+                <div class="title">Bayesian multi-model comparison</div>
                 
               </div>
             </a>
diff --git a/docs/source/bayes_description.rst b/docs/source/bayes_description.rst
index 1c72a3e9987ca89da79132dece7ba4626a218e96..0cb36d10f808a92e14d29abc01b9a7fd6883466b 100644
--- a/docs/source/bayes_description.rst
+++ b/docs/source/bayes_description.rst
@@ -87,4 +87,35 @@ Then we run the inference.
 
 >>> BayesObj.create_inference()
 
-If the output directory ``BayesObj.out_dir`` is not set otherwise, the outputs are written into the folder ``
\ No newline at end of file
+If the output directory ``BayesObj.out_dir`` is not set otherwise, the outputs are written into the folder ``Outputs_Bayes_model_Calib``.
+This folder includes the posterior distribution of the input parameters, as well as the predictions resulting from the mean of the posterior.
+For inference with MCMC, chain diagnostics are also written out in the console.
+
+.. container:: twocol
+
+   .. container:: leftside
+   
+      .. code-block:: py
+
+         ---------------Posterior diagnostics---------------
+         Mean auto-correlation time: 2.057
+         Thin: 1
+         Burn-in: 4
+         Flat chain shape: (13380, 1)
+         Mean acceptance fraction*: 0.752
+         Gelman-Rubin Test**:  [1.001]
+
+         * This value must lay between 0.234 and 0.5.
+         ** These values must be smaller than 1.1.
+         --------------------------------------------------
+		 
+   .. container:: rightside
+
+      .. image:: ../../examples/user_guide/Outputs_Bayes_model_Calib/Posterior_Dist_model_emulator.pdf
+         :width: 400
+         :alt: Posterior distribution of the input parameter
+		 
+      .. image:: ../../examples/user_guide/Outputs_Bayes_model_Calib/Post_Prior_Perd_model_emulator_A.pdf
+         :width: 400
+         :alt: Comparison of posterior prediction to the observation
+		 
\ No newline at end of file
diff --git a/docs/source/bmc_description.rst b/docs/source/bmc_description.rst
index 10e73bd1e819ad67df4fe48247a2bcf26fe698a7..b3eaf86c2ca702ffa9781de4f6f3224f87c479fb 100644
--- a/docs/source/bmc_description.rst
+++ b/docs/source/bmc_description.rst
@@ -1,7 +1,22 @@
 Bayesian multi-model comparison
 *******************************
+.. container:: twocol
 
-.. image:: ../diagrams/bayesian_model_comparison.png
-   :width: 400
-   :alt: UML diagram for classes related to Bayesian multi-model comparison.
+   .. container:: leftside
+   
+      Bayesvalidrox provides three distinct methods to compare sets of models against each other given some observation of the outputs, Bayes' Factors, model weights and confusion matrices.
+      These are contained within the class :any:`bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison` and can be called one-at-a-time with their respective functions, or consecutively with the function ``model_comparison_all()``.
+	  
+      
+   .. container:: rightside
+   
+      .. image:: ../diagrams/bayesian_model_comparison.png
+         :width: 400
+         :alt: UML diagram for classes related to Bayesian multi-model comparison.
 
+
+Example
+=======
+To perform model comparison, we first need to define the set of competing models.
+For this, we create two additional models based on the example model from :any:`model_description`.
+The first of these models 
\ No newline at end of file
diff --git a/examples/user_guide/example_user_guide.py b/examples/user_guide/example_user_guide.py
index 3be56216f53be165b7284e1ef766380c5d3a2677..53816d18a5cdf4f4ca4c64c06283154caabfbaf4 100644
--- a/examples/user_guide/example_user_guide.py
+++ b/examples/user_guide/example_user_guide.py
@@ -50,11 +50,13 @@ if __name__ == '__main__':
     ExpDesign.plot_samples(samples)
     
     #### Models
+    x_values = np.arange(0,10,1)/10
     Model = PyLinkForwardModel()
     Model.link_type = 'Function'
     Model.py_file = 'model'
     Model.name = 'model'
     Model.Output.names = ['A', 'B']
+    Model.func_args = {'x_values':x_values}
     
     #output, samples = Model.run_model_parallel(samples, mp = True)
     
diff --git a/examples/user_guide/model.py b/examples/user_guide/model.py
index 2bb1b011fae7c82bf299f4a92ba6787dd58a0f2b..4d0190fd0e6da7f1034d13a340addfe4901173de 100644
--- a/examples/user_guide/model.py
+++ b/examples/user_guide/model.py
@@ -6,8 +6,8 @@ A simple model example for the BVR user guide.
 """
 import numpy as np
 
-def model(samples):
-    samples = samples[0]
+def model(samples, x_values):
+    samples = samples[0]*x_values
     square = np.power(samples, 2)
-    outputs = {'A': samples, 'B': square, 'x_values': [0]}
+    outputs = {'A': samples, 'B': square, 'x_values': x_values}
     return outputs
\ No newline at end of file
diff --git a/src/bayesvalidrox/bayes_inference/bayes_inference.py b/src/bayesvalidrox/bayes_inference/bayes_inference.py
index 5bc144960907c7dbdd8fffa2587453d9c8f246f3..e0e234374a899aef11fff243bf7803e8253b50a1 100644
--- a/src/bayesvalidrox/bayes_inference/bayes_inference.py
+++ b/src/bayesvalidrox/bayes_inference/bayes_inference.py
@@ -759,7 +759,8 @@ class BayesInference:
                     # Perturb the data
                     std = np.nanstd(obs_data[:, idx])
                     if std == 0:
-                        print('Note: Use std=0.01 for perturbation')
+                        if itrIdx == 1:
+                            print('Note: Use std=0.01 for perturbation')
                         std = 0.001
                     noise = std * noise_level
                     data[:, idx] = np.add(
@@ -872,7 +873,7 @@ class BayesInference:
             # Add the std of the PCE if an emulator is used
             if self.emulator:
                 if std is not None:
-                    tot_sigma2s += std[out] ** 2
+                    tot_sigma2s = tot_sigma2s+std[out] ** 2
 
             # Select the data points to compare
             try:
@@ -1191,7 +1192,7 @@ class BayesInference:
                     else:
                         stdPCE = post_pred_std[var][i]
                     # Expected value of variance (Assump: i.i.d stds)
-                    cov += np.diag(stdPCE ** 2)
+                    cov = cov + np.diag(stdPCE ** 2)
 
                 # Sample a multivariate normal distribution with mean of
                 # posterior prediction and variance of cov
diff --git a/src/bayesvalidrox/bayes_inference/mcmc.py b/src/bayesvalidrox/bayes_inference/mcmc.py
index ad7c9f1e5e6c073f0d80746091e5ba3f70c4bc38..973abea7112a2d8999470ffd0123a76a94edbd0d 100755
--- a/src/bayesvalidrox/bayes_inference/mcmc.py
+++ b/src/bayesvalidrox/bayes_inference/mcmc.py
@@ -361,6 +361,10 @@ class MCMC:
         # Set up the backend and clear it in case the file already exists
         backend = emcee.backends.HDFBackend(f"{self.out_dir}/emcee_sampler.h5")
         backend.reset(self.nwalkers, ndim)
+        
+        # Recheck the size of the initsamples
+        if len(initsamples.shape)<2:
+            initsamples = np.swapaxes(np.array([initsamples]),0,1)
 
         # Define emcee sampler
         # Here we'll set up the computation. emcee combines multiple "walkers",
@@ -880,7 +884,7 @@ class MCMC:
             # Add the std of the PCE if an emulator is used
             if self.emulator:
                 if std is not None:
-                    tot_sigma2s += std[out] ** 2
+                    tot_sigma2s = tot_sigma2s + std[out] ** 2
 
             # Select the data points to compare
             try:
diff --git a/src/bayesvalidrox/pylink/pylink.py b/src/bayesvalidrox/pylink/pylink.py
index 64ad87b7b35fe948b1c68221be12ebbe3ca8f91a..146cfbf28e0e082c43b1018c96c4e63d60b038d9 100644
--- a/src/bayesvalidrox/pylink/pylink.py
+++ b/src/bayesvalidrox/pylink/pylink.py
@@ -695,6 +695,8 @@ class PyLinkForwardModel(object):
                 try:
                     oldEDY = np.array(file[f'EDY/{var}/adaptive_{key_str}'])
                     del file[f'EDY/{var}/adaptive_{key_str}']
+                    print(oldEDY.shape)
+                    print(all_outputs[var].shape)
                     data = np.vstack((oldEDY, all_outputs[var]))
                 except KeyError:
                     data = all_outputs[var]