updating, including Udos comments

JohannesBuchner · Nov 21, 2013 · 1d856b6 · 1d856b6
1 parent 1b0baff
commit 1d856b6
Show file tree

Hide file tree

Showing 9 changed files with 130 additions and 33 deletions.
diff --git a/doc/source/conf.py b/doc/source/conf.py
@@ -243,4 +243,5 @@
 
 
 # Example configuration for intersphinx: refer to the Python standard library.
-intersphinx_mapping = {'http://docs.python.org/': None}
+intersphinx_mapping = {} #'http://docs.python.org/': None}
+
diff --git a/doc/source/example1.rst b/doc/source/example1.rst
@@ -1,6 +1,10 @@
 Example 1: One-dimensional multi-modal problem
 ===============================================
 
+Get a copy of the `tutorial example code <https://github.com/JohannesBuchner/pymultinest-tutorial>`_::
+
+   $ git clone https://github.com/JohannesBuchner/pymultinest-tutorial
+
 In the folder example1, find the file 1d_multimodal.py. It illustrates how to call pymultinest with
 
 * one dimension only

diff --git a/doc/source/example2.rst b/doc/source/example2.rst
@@ -25,7 +25,8 @@ Your task
 3. What is the evidence for this model?
 4. **Extend the model to 2 gaussian lines.**
 5. Are 2 gaussian lines preferred? I.e. is the evidence higher?
-6. Analyse the other datasets. Are the results the same?
+6. Are 3 gaussian lines preferred?
+7. Analyse the other datasets. Are the results the same?
 
 Continue with :doc:`example3` ...
 
diff --git a/doc/source/example3.rst b/doc/source/example3.rst
@@ -1,7 +1,7 @@
 Example 3: Gaussian Emission lines - correlations
 ==================================================
 
-In :doc:example2, we analysed emission lines. We now have the derived parameters
+In :doc:`example2`, we analysed emission lines. We now have the derived parameters
 distribution for each spectrum.
 
 * Are the line widths and heights correlated?
@@ -13,15 +13,18 @@ How would you answer these questions?
 Keep in mind, that you want to take into account the uncertainties in the
 derived parameters!
 
-
 Next
------
+------
+
+a) For inspiration to the problem above, look at `SysCorr <http://johannesbuchner.github.io/syscorr/index.html>`_ and continue with the example there.
+b) Solve the `light-house problem <http://www.gps.caltech.edu/classes/ge193/practicals/practical3/Lighthouse.pdf>`_ with one light house, and with two light houses. Apply model selection!
+c) You may want to implement your own problem using pymultinest.
 
-* You may want to implement your own problem using pymultinest.
-* For inspiration, to the problem above, look at `SysCorr <http://johannesbuchner.github.io/syscorr/index.html>`_ and continue with its example.
+Links
+-------
+* `jbopt <http://johannesbuchner.github.io/jbopt/index.html>`_ is a cross-algorithm parameter space exploration toolkit. Check out the code example!
 * `PyMultiNest documentation <http://johannesbuchner.github.io/pymultinest/index.html>`_
-* Also check out pycuba, a integration library.
-* `jbopt <http://johannesbuchner.github.io/jbopt/index.html>`_ is a cross-algorithm parameter space exploration toolkit. Check out the code example.
+* Also check out pycuba, a Monte Carlo integration library.
 
 
 
diff --git a/doc/source/index.rst b/doc/source/index.rst
@@ -10,7 +10,8 @@ It should kickstart you to
 * run pymultinest
 * visualize and interpret the results
 
-Make sure you have :doc:`pymultinest installed <install>`. Then, **go get started with** :doc:`Example 1 <example1>`!
+Make sure you have :doc:`pymultinest installed <install>` correctly.
+Then, **go get started with** :doc:`Example 1 <example1>`!
 
 Contents
 ---------------

diff --git a/doc/source/install.rst b/doc/source/install.rst
@@ -6,21 +6,18 @@ On the school computers
 
 1. Log in, and run the bash shell::
 
-	[school08@naf-school01]~% bash
-	school08@naf-school01 ~ $ 
+	$ ssh -Y schoolNN@naf-school01.desy.de
+	[schoolNN@naf-school01]~% bash
+	bash-4.1$ 
 
 2. Load the environment::
 	
-	$ . /afs/desy.de/group/school/mc-school/setup_pymultinest.sh
-
-3. Test it::
-
-	$ mkdir test
-	$ cd test
-	$ python /afs/desy.de/group/school/mc-school/multinest-install/PyMultiNest/pymultinest_demo_minimal.py
-	$ multinest_marginals.py chains/1-
-
+	bash-4.1$ source /afs/desy.de/group/school/mc-school/setup_pymultinest.sh
+	installing pymultinest ... installation successful
+	configuring environment and testing ... ok
+	schoolNN@naf-school01 ~ $
 
+Go start with Example 1. Do not waste time installing on your own computer before having finished Example 1.
 
 On your own computer
 ----------------------------

diff --git a/example1/1d_multimodal.py b/example1/1d_multimodal.py
@@ -20,7 +20,7 @@ def loglike(cube, ndim, nparams):
 	# get the current parameter (is between 0:2 now)
 	pos = cube[0]
 	likelihood = exp(-0.5 * ((pos - positions) / width)**2) / (2*pi*width**2)**0.5
-	return log(likelihood.sum())
+	return log(likelihood.mean())
 
 # number of dimensions our problem has
 parameters = ["position"]
@@ -37,5 +37,6 @@ def loglike(cube, ndim, nparams):
 #
 # then open the file 1_1d_multimodal_outmarg.pdf
 #
-# Btw, ln(ev) should be ln(6 / 2)
+# Btw, ln(ev) should be ln(1 / 2)
+
 
diff --git a/example2/lines.py b/example2/lines.py
@@ -61,7 +61,11 @@ def loglike(cube, ndim, nparams):
 
 a_lnZ = a.get_stats()['global evidence']
 print 
-print '  log p(model = 1 line ) = %.1f%s' % (a_lnZ / log(10),
+print '************************'
+print 'MAIN RESULT: Evidence Z '
+print '************************'
+print '  log Z for model with 1 line = %.1f' % (a_lnZ / log(10))
+print
 
 # TODO: implement a model with 2 lines?
 

diff --git a/slides/index.html b/slides/index.html
@@ -32,6 +32,21 @@
 		padding: 0.2em 0.5em;
 		border-bottom: 1px dashed #CCC;
 		}
+
+.checkboxlist li {
+	list-style: none;
+}
+.checkboxlist li:before
+{
+    content: "\2610";
+    margin-right:5px;
+}
+
+.checkboxlist li:hover:before
+{
+    content: "\2611";
+    margin-right:5px;
+}
 		</style>
 
 		<script type="text/javascript">
@@ -51,17 +66,62 @@ <h3>Casual parameter estimation and model selection</h3>
 	<p style="font-size: 0.75em">Max Planck Institute for Extraterrestrial Physics
 	<p style="font-size: 0.75em">November 2013
 </section>
+
 <section>
 	<h2>About me</h2>
 	<ul><li>implemented MCMC sampler for Bachelor thesis
 	<li>since then, 5 years of experience with Monte Carlo methods for Bayesian inference
-	<li>Numerical Likelihood functions, low-dimensional (&lt;20)
+	<li>Numerical Likelihood functions (0.1-5s), low-dimensional (&lt;20)
 	<li>Research on accreting supermassive black hole in X-ray (Poisson spectra)
 	<li>Recent interest: smooth field reconstruction with numerical likelihoods (20-500 dimensions)
+	</ul>
+	<p style="font-size: 0.5em"><a href="https://www.mpe.mpg.de/~jbuchner/">https://www.mpe.mpg.de/~jbuchner/</a> -- Johannes Buchner
+</section>
+
+<section>
+	<h2>Go-to Methods</h2>
+	<div style="text-align: left">
+	(for numerical likelihoods)
+	<h3>Parameter estimation</h3>
+	<ul>
+	<li>Optimize to maximum (ML/MAP)
+	<li>explore around it with MCMC
+	<li>High-dimensional, misbehaved: MCMC (?), HMC (?)
+	<li>
+	</ul>
+	<h3>Model selection</h3>
+	<ul>
+	<li>High-dimensional: 
+	<li>Low-dimensional: 
+	<li>Nested models: 
+	</ul>
+	</div>
+</section>
+
+<section>
+	<h2>Tools so far</h2>
+	<div style="text-align: left">
+	(for numerical likelihoods)
+	<h3>Parameter estimation</h3>
+	<ul>
+	<li>Optimize to maximum (ML/MAP)
+	<li>explore around it with MCMC
+	<li>High-dimensional, misbehaved: MCMC (?), HMC (?)
+	<li>Low-dimensional, multi-modal: MultiNest
+	</ul>
+	<h3>Model selection</h3>
+	<ul>
+	<li>High-dimensional: give up
+	<li>Low-dimensional (&lt;20), multi-modal: MultiNest
+	<li>Nested models: AIC + DE
+	</ul>
+	also for Low-dimensional, multi-modal: MultiNest
+	</div>
 </section>
 
 <section>
 	<h2>What will we do today?</h2>
+	Goal: solving <script type="math/tex">Z</script> integrals
 	<ul>
 	<li>Write likelihood functions
 	<li>Write prior functions
@@ -73,9 +133,11 @@ <h2>What will we do today?</h2>
 <section>
 	<h2>Software: PyMultiNest</h2>
 	<ul>
-	<li>based on MultiNest: written by Farhan Feroz and Mike Hobson
+	<li>based on MultiNest: written by Farhan Feroz and Mike Hobson (2007)
+	<li>Finds clusters -> sampling from ellipses
 	<li>Python instead of writing Fortran or C functions
 	<li>parses output, and does a bit of plotting
+	<li>Also produces "Markov Chain" for uncertainty propagation
 	</ul>
 </section>
 
@@ -92,14 +154,23 @@ <h2>Prior functions: A math trick</h2>
 
 	<div class="fragment"><ul><li>transformation through inverse of CDF
 	<li>compresses unimportant regions
-	<li>"native units" - can also do this in MCMC!
+	<li>"native units": <script type="math/tex">P(\theta|D)\propto \int_0^1{P(D|u) du} </script>
+	<li>can also do this in MCMC!
+	</ul></div>
+</section>
+<section>
+	<h2>Prior functions: A math trick</h2>
+	<ul>
+	<li>Transform from unit cube to parameter space
+	<li>Using inverse CDF of prior
 	</ul>
-
+	<img src="prior_transform_uniform.png" style="background-color: white;" />
+	<img src="prior_transform_loguniform.png" style="background-color: white;"/>
 	<pre><code data-trim class="python">
 def prior(cube, ndim, nparams):
-	cube[0] = cube[0] * 2
-	cube[1] = 10**(cube[1] * 10 - 5)
-</code></pre></div>
+	cube[0] = cube[0] * (3 - 1) + 1
+	cube[1] = 10**(cube[1] * (1 + 0.5) - 1)
+</code></pre>
 </section>
 
 
@@ -125,11 +196,25 @@ <h2>Shortest Code Example</h2>
 <section>
 	<h2>Tutorial</h2>
 	<a href="http://johannesbuchner.github.io/pymultinest-tutorial/" target="_window">http://johannesbuchner.github.io/pymultinest-tutorial/</a>
+	<pre><code data-trim class="bash">$ ssh -Y schoolNN@naf-school01.desy.de
+$ bash
+$ source /afs/desy.de/group/school/mc-school/setup_pymultinest.sh
+$ git clone https://github.com/JohannesBuchner/pymultinest-tutorial</code></pre>
+	<ul class="checkboxlist">
+	<li>Example 1: <i>1d multi-modal problem</i>
+	<li>Example 2: <i>Spectral line analysis</i> -- 1 line or 2 lines?
+	<li>Example 3: Hierarchical Bayes, Your own, Lighthouse problem, further reading
+	</ul>
 </section>
 
 <section>
-	<h2>References</h2>
-
+	<h2>Final points</h2>
+	<ul>
+	<li>Correlation of parameters from posterior samples <a href="http://johannesbuchner.github.io/syscorr/index.html">SysCorr</a>
+	<li>Throw multiple algorithms against problem (<a href="http://johannesbuchner.github.io/jbopt/index.html">jbopt</a>)
+	<li>Fully automated model selection, but is model a good one? Systematic errors? Confidence on model choice?
+	<li>PyMultiNest reference: Buchner et al (in prep), MultiNest: arXiv:0704.3704, arXiv:0809.3437 & arXiv:1306.2144
+	</ul>
 </section>
 
 			</div>