From d0629ca6a43752bcfbc9c3f8b1fb72eda09fdd59 Mon Sep 17 00:00:00 2001
From: kohlhaasrebecca <rebecca.kohlhaas@outlook.com>
Date: Wed, 17 Jul 2024 10:15:27 +0200
Subject: [PATCH] User guide BayesInf finished

Finished the example for BayesInf for the user guide and fixed some small bugs for MCMC with a single input.
Started working on the user guide for BMC, but issue in AL with changes in the model
---
 ...> .coverage.DESKTOP-ATMEKSV.29620.XFvzCgcx | Bin
 docs/build/doctrees/bayes_description.doctree | Bin 16927 -> 25020 bytes
 docs/build/doctrees/bmc_description.doctree   | Bin 2910 -> 6909 bytes
 docs/build/doctrees/environment.pickle        | Bin 3124130 -> 3138059 bytes
 ...erence.bayes_inference.BayesInference.html |   3 +-
 ...idrox.bayes_inference.bayes_inference.html |   3 +-
 ...model_comparison.BayesModelComparison.html |   3 +-
 ...ayes_inference.bayes_model_comparison.html |   3 +-
 ...yes_inference.discrepancy.Discrepancy.html |   3 +-
 ...svalidrox.bayes_inference.discrepancy.html |   3 +-
 .../bayesvalidrox.bayes_inference.html        |   3 +-
 ...yesvalidrox.bayes_inference.mcmc.MCMC.html |   3 +-
 ...rox.bayes_inference.mcmc.gelman_rubin.html |   3 +-
 .../bayesvalidrox.bayes_inference.mcmc.html   |   3 +-
 .../html/_autosummary/bayesvalidrox.html      |   3 +-
 .../bayesvalidrox.post_processing.html        |   3 +-
 ...essing.post_processing.PostProcessing.html |   3 +-
 ...idrox.post_processing.post_processing.html |   3 +-
 .../_autosummary/bayesvalidrox.pylink.html    |   3 +-
 ...drox.pylink.pylink.PyLinkForwardModel.html |   3 +-
 .../bayesvalidrox.pylink.pylink.html          |   3 +-
 ...esvalidrox.pylink.pylink.within_range.html |   3 +-
 ....surrogate_models.adaptPlot.adaptPlot.html |   3 +-
 ...esvalidrox.surrogate_models.adaptPlot.html |   3 +-
 ...apoly_construction.apoly_construction.html |   3 +-
 ...x.surrogate_models.apoly_construction.html |   3 +-
 ...bayes_linear.BayesianLinearRegression.html |   3 +-
 ...odels.bayes_linear.EBLinearRegression.html |   3 +-
 ...odels.bayes_linear.VBLinearRegression.html |   3 +-
 ...rogate_models.bayes_linear.gamma_mean.html |   3 +-
 ...alidrox.surrogate_models.bayes_linear.html |   3 +-
 ...lidrox.surrogate_models.engine.Engine.html |   3 +-
 ...gate_models.engine.hellinger_distance.html |   3 +-
 ...bayesvalidrox.surrogate_models.engine.html |   3 +-
 ...lidrox.surrogate_models.engine.logpdf.html |   3 +-
 ...rox.surrogate_models.engine.subdomain.html |   3 +-
 ...te_models.eval_rec_rule.eval_rec_rule.html |   3 +-
 ...eval_rec_rule.eval_rec_rule_arbitrary.html |   3 +-
 ..._models.eval_rec_rule.eval_univ_basis.html |   3 +-
 ...lidrox.surrogate_models.eval_rec_rule.html |   3 +-
 ..._models.eval_rec_rule.poly_rec_coeffs.html |   3 +-
 ...rrogate_models.exp_designs.ExpDesigns.html |   3 +-
 ...ogate_models.exp_designs.check_ranges.html |   3 +-
 ...validrox.surrogate_models.exp_designs.html |   3 +-
 ...rogate_models.exploration.Exploration.html |   3 +-
 ...validrox.surrogate_models.exploration.html |   3 +-
 ...ogate_models.glexindex.cross_truncate.html |   3 +-
 ....surrogate_models.glexindex.glexindex.html |   3 +-
 ...esvalidrox.surrogate_models.glexindex.html |   3 +-
 .../bayesvalidrox.surrogate_models.html       |   3 +-
 ...rrogate_models.input_space.InputSpace.html |   3 +-
 ...validrox.surrogate_models.input_space.html |   3 +-
 ...alidrox.surrogate_models.inputs.Input.html |   3 +-
 ...drox.surrogate_models.inputs.Marginal.html |   3 +-
 ...bayesvalidrox.surrogate_models.inputs.html |   3 +-
 ...ing_pursuit.OrthogonalMatchingPursuit.html |   3 +-
 ...dels.orthogonal_matching_pursuit.corr.html |   3 +-
 ...te_models.orthogonal_matching_pursuit.html |   3 +-
 ...models.reg_fast_ard.RegressionFastARD.html |   3 +-
 ...alidrox.surrogate_models.reg_fast_ard.html |   3 +-
 ...models.reg_fast_ard.update_precisions.html |   3 +-
 ...eg_fast_laplace.RegressionFastLaplace.html |   3 +-
 ...rox.surrogate_models.reg_fast_laplace.html |   3 +-
 ...ate_models.surrogate_models.MetaModel.html |   3 +-
 ...els.surrogate_models.corr_loocv_error.html |   3 +-
 ...te_models.surrogate_models.create_psi.html |   3 +-
 ...gate_models.gaussian_process_emulator.html |   3 +-
 ...rox.surrogate_models.surrogate_models.html |   3 +-
 .../html/_sources/bayes_description.rst.txt   |  59 ++++++++++++++++++
 .../html/_sources/bmc_description.rst.txt     |  21 ++++++-
 docs/build/html/al_description.html           |   3 +-
 docs/build/html/analyticalfunction.html       |   3 +-
 docs/build/html/api.html                      |   3 +-
 docs/build/html/bayes_description.html        |  53 +++++++++++++++-
 docs/build/html/beam.html                     |   3 +-
 docs/build/html/bmc_description.html          |  39 +++++++++++-
 docs/build/html/borehole.html                 |   3 +-
 docs/build/html/examples.html                 |   3 +-
 docs/build/html/ishigami.html                 |   3 +-
 docs/build/html/modelcomparison.html          |   3 +-
 docs/build/html/ohaganfunction.html           |   3 +-
 docs/build/html/pollution.html                |   3 +-
 docs/build/html/searchindex.js                |   2 +-
 docs/build/html/surrogate_description.html    |   3 +-
 docs/build/html/tutorial.html                 |  11 ++--
 docs/source/bayes_description.rst             |  33 +++++++++-
 docs/source/bmc_description.rst               |  21 ++++++-
 examples/user_guide/example_user_guide.py     |   2 +
 examples/user_guide/model.py                  |   6 +-
 .../bayes_inference/bayes_inference.py        |   7 ++-
 src/bayesvalidrox/bayes_inference/mcmc.py     |   6 +-
 src/bayesvalidrox/pylink/pylink.py            |   2 +
 92 files changed, 388 insertions(+), 99 deletions(-)
 rename .coverage.DESKTOP-ATMEKSV.10052.XHqUUOFx => .coverage.DESKTOP-ATMEKSV.29620.XFvzCgcx (100%)

diff --git a/.coverage.DESKTOP-ATMEKSV.10052.XHqUUOFx b/.coverage.DESKTOP-ATMEKSV.29620.XFvzCgcx
similarity index 100%
rename from .coverage.DESKTOP-ATMEKSV.10052.XHqUUOFx
rename to .coverage.DESKTOP-ATMEKSV.29620.XFvzCgcx
diff --git a/docs/build/doctrees/bayes_description.doctree b/docs/build/doctrees/bayes_description.doctree
index c98ceb2eb03163cb759d71f1023fd5d1ef36aff3..7ecf21c6be10ecf165c848a850df703d88514ba5 100644
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delta 173
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diff --git a/docs/build/doctrees/bmc_description.doctree b/docs/build/doctrees/bmc_description.doctree
index 33dc7d173f129329f4e812774fb1f08c1477a449..320a137b1447b6f76c7a0c1f453029191acb68d1 100644
GIT binary patch
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delta 118
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diff --git a/docs/build/doctrees/environment.pickle b/docs/build/doctrees/environment.pickle
index c92835fb3f4d66829bf05a6f3539006cd13bbf6c..dd1a295178cd9c0e3bdb5158f5735c8a69d2c1a7 100644
GIT binary patch
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diff --git a/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_inference.BayesInference.html b/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_inference.BayesInference.html
index a8fbf9952..d6ae664d3 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_inference.BayesInference.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_inference.BayesInference.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.bayes_inference.bayes_inference.html b/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_inference.html
index d5f4bdc76..be2a80de6 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_inference.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_inference.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.bayes_inference.bayes_model_comparison.BayesModelComparison.html b/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison.html
index b2a554f9d..8c36c6bea 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_model_comparison.BayesModelComparison.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.bayes_inference.bayes_model_comparison.html b/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_model_comparison.html
index 83a052126..0180e21c6 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_model_comparison.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.bayes_model_comparison.html
@@ -170,7 +170,8 @@
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--- a/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.discrepancy.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.bayes_inference.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.pylink.pylink.html
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--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.adaptPlot.adaptPlot.html
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+++ 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>
+<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.EBLinearRegression.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.EBLinearRegression.html
index 1e19d3665..e5b8b3aaf 100644
--- 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 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.VBLinearRegression.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.VBLinearRegression.html
index 3ba8a66cb..49002d5f3 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 c3b2d5667..f9446b9c3 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>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.html
index 5d1164c23..12a692322 100644
--- 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 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.Engine.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.Engine.html
index 563940f5f..bc8c4c8df 100644
--- 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>
diff --git a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.hellinger_distance.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.hellinger_distance.html
index d4d269e7f..1468932d5 100644
--- 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
index 885ebd13a..f43c214e2 100644
--- 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>
 </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.logpdf.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.logpdf.html
index d1ef23527..edd183342 100644
--- 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>
 </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.subdomain.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.subdomain.html
index 9e48ba3c3..6d630a958 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.subdomain.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.engine.subdomain.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.eval_rec_rule.eval_rec_rule.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule.html
index cac4d998e..e081f64c3 100644
--- 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 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.eval_rec_rule.eval_rec_rule_arbitrary.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_rec_rule_arbitrary.html
index dde4517e0..936d75c87 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 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.eval_rec_rule.eval_univ_basis.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_univ_basis.html
index cc0f1d31c..8a4325678 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_univ_basis.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.eval_univ_basis.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.eval_rec_rule.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.html
index 58709347d..e566e9fc9 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.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 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.eval_rec_rule.poly_rec_coeffs.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.eval_rec_rule.poly_rec_coeffs.html
index b13d05c48..211d11ec9 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
@@ -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.exp_designs.ExpDesigns.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.ExpDesigns.html
index 6548c9a39..ebb205a5b 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.ExpDesigns.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.ExpDesigns.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.exp_designs.check_ranges.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.check_ranges.html
index c9556e431..3f8c99c60 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.check_ranges.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.check_ranges.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.exp_designs.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.html
index 0a54834e0..12f3e3b7b 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exp_designs.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.exploration.Exploration.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.Exploration.html
index 4496b2d8f..bfc9e4887 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.Exploration.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.Exploration.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.exploration.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.html
index 5482569e1..4fe52523a 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.exploration.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.glexindex.cross_truncate.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.cross_truncate.html
index 5a03208c8..ef1e59d9f 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 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.glexindex.glexindex.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.glexindex.html
index a950df2ff..128c42630 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 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.glexindex.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.glexindex.html
index 96400f333..f22f12377 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>
 </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.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.html
index 4312aa252..551916f8f 100644
--- 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 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.input_space.InputSpace.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.input_space.InputSpace.html
index 842557588..f9d2df3bd 100644
--- 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>
 </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.input_space.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.input_space.html
index cc003dd63..7c8cd9299 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.input_space.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.input_space.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.inputs.Input.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.Input.html
index 95f8b8e45..c3b3d9d99 100644
--- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.Input.html
+++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.Input.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.inputs.Marginal.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.Marginal.html
index fca0dcb0d..fcb16dad3 100644
--- 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>
 </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.inputs.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.inputs.html
index d5c3b12c1..4e16820e3 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 @@
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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.orthogonal_matching_pursuit.OrthogonalMatchingPursuit.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.OrthogonalMatchingPursuit.html
index 43f20bf42..7e9829327 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 @@
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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.orthogonal_matching_pursuit.corr.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.corr.html
index 274d8319d..8f61f3d06 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 @@
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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.orthogonal_matching_pursuit.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.orthogonal_matching_pursuit.html
index f159c07b7..17f469e71 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 @@
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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.reg_fast_ard.RegressionFastARD.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.RegressionFastARD.html
index 35ea14b81..9dd1a74ff 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>
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 <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 f1a15392d..dcd0820e6 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 @@
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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.reg_fast_ard.update_precisions.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_ard.update_precisions.html
index ff1c030d1..05bcfb125 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 @@
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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.reg_fast_laplace.RegressionFastLaplace.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.RegressionFastLaplace.html
index dc6b45be7..5ea393418 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 @@
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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.reg_fast_laplace.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.reg_fast_laplace.html
index 39bed6efb..8ed5c18d5 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 @@
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 <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 07bf13ba0..b19b79684 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 a047d2ad8..85883cb84 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 1b72a962c..4a66eb692 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 560f6c733..a38aa4e63 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 82a65402e..bb5eaba6c 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 0406162ed..0cb36d10f 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 10e73bd1e..b3eaf86c2 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 78a5f609e..e3cde5ecd 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 42509cf38..799f0350a 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 d853aff4e..7f918265a 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 4d5cfd6c6..487cb49bc 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 6c82f54b9..64c4a4c02 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 03d4552b2..15dc59943 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 eafbe8618..683c27d0e 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 9d6b6cce8..4c621310a 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 06d5b7d8c..dcf8bda0b 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 723a66ed1..472be01bb 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 cfe645ff0..e7b755875 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>
+<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/pollution.html b/docs/build/html/pollution.html
index 4b71758ef..e7ae39a11 100644
--- a/docs/build/html/pollution.html
+++ b/docs/build/html/pollution.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/searchindex.js b/docs/build/html/searchindex.js
index fec129dec..a142440be 100644
--- a/docs/build/html/searchindex.js
+++ b/docs/build/html/searchindex.js
@@ -1 +1 @@
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\ No newline at end of file
diff --git a/docs/build/html/surrogate_description.html b/docs/build/html/surrogate_description.html
index c48db82a4..db4708ce6 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 820f6d348..f4c941291 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">
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               <div class="page-info">
                 <div class="context">
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-                <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 1c72a3e99..0cb36d10f 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 10e73bd1e..b3eaf86c2 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 3be56216f..53816d18a 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 2bb1b011f..4d0190fd0 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 5bc144960..e0e234374 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 ad7c9f1e5..973abea71 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 64ad87b7b..146cfbf28 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]
-- 
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