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rbouckaert committed Mar 24, 2019
1 parent ba3b6ac commit a72fb796ae1e561c52a3e5c1e299b17574d211e4
Showing with 22 additions and 15 deletions.
  1. +5 −3 README.md
  2. +17 −12 main.tex
@@ -29,7 +29,7 @@ Note that sometimes a factor 2 is used for multiplying BFs, so when comparing BF
**Nested sampling** is an algorithm that works as follows:

* randomly sample `N` points from the prior
* while not coverged
* while not converged
* pick the point with the lowest likelihood L<sub>min</sub>, and save to log file
* replace the point with a new point randomly sampled from the prior using an MCMC chain of `subChainLength` samples __under the condition that the likelihood is at least L<sub>min</sub>__

@@ -319,7 +319,9 @@ The parallel implementation makes it possible to run many particles in parallel,

The NS package has a `NSLogAnalyser` application that you can run via the menu `File/Launch apps` in BEAUti -- a window pops up where you select the `NSLogAnalyser`, and a dialog shows you various options to fill in. You can also run it from the command line on OS X or Linux using

`/path/to/beast/bin/applauncher NSLogAnalyser -N 1 -log xyz.log`
```
/path/to/beast/bin/applauncher NSLogAnalyser -N 1 -log xyz.log
```

where the argument after `N` is the `particleCount` you specified in the XML, and `xyz.log` the trace log produced by the NS run.

@@ -345,7 +347,7 @@ The ESSs in Tracer of log files with the posterior samples are meaningless, beca
- Nested sampling website and documentation: [https://github.com/BEAST2-Dev/nested-sampling](https://github.com/BEAST2-Dev/nested-sampling)
- Join the BEAST user discussion: [http://groups.google.com/group/beast-users](http://groups.google.com/group/beast-users)

----


# Relevant References

@@ -25,18 +25,19 @@
\begin{center}

% Enter the name of your tutorial here
\textbf{\LARGE Tutorial using BEAST v2.5.2}\\\vspace{2mm}
\textbf{\textcolor{mycol}{\LARGE Model selection with nested sampling}}\\\vspace{2mm}

% Enter a short description of your tutorial here
\textbf{\textcolor{mycol}{\Large Model selection}}\\
\textbf{\Large Tutorial using BEAST v2.5.2}\\

\vspace{4mm}

% Enter the names of all the authors here
{\Large {\em Remco Bouckaert}}
\vspace{-2mm}
\end{center}

Model selection with nested sampling


%%%%%%%%%%%%%%%%%
% Tutorial body %
@@ -55,28 +56,30 @@ \section{Background}\label{background}
tutorial gives some guidelines on how to select the model that is most
appropriate for your analysis.

\vspace{-2mm}
Bayesian model selection is based on estimating the marginal likelihood:
the term forming the denominator in Bayes formula. This is generally a
computationally intensive task and there are several ways to estimate
them. Here, we concentrate on nested sampling as a way to estimate the
marginal likelihood as well as the uncertainty in that estimate.

\vspace{-2mm}
Say, we have two models, M1 and M2, and estimates of the (log) marginal
likelihood, ML1 and ML2, then we can calculate the Bayes factor, which
is the fraction BF=ML1/ML2 (or in log space, the difference log(BF) =
log(ML1)-log(ML2)). If BF is larger than 1, model M1 is favoured, and
otherwise M2 is favoured. How much it is favoured can be found in the
following table \citep{kass1995bayes}:

\begin{figure}[b]
\begin{figure}[h]
\centering
\includegraphics[width=0.800000\textwidth]{figures/BFs.png}
\caption{Bayes factor support.}
\end{figure}

Note that sometimes a factor 2 is used for multiplying BFs, so when
comparing BFs from different publications, be aware which definition
that was used.
comparing BFs from different publications, be aware which definition was
used.

\textbf{Nested sampling} is an algorithm that works as follows:

@@ -85,16 +88,16 @@ \section{Background}\label{background}
\item
randomly sample \lstinline!N! points from the prior
\item
while not coverged
while not converged

\begin{itemize}

\item
pick the point with the lowest likelihood Lmin, and save to log file
pick the point with the lowest likelihood $L_{min}$, and save to log file
\item
replace the point with a new point randomly sampled from the prior
using an MCMC chain of \lstinline!subChainLength! samples
\textbf{under the condition that the likelihood is at least Lmin}
\textbf{under the condition that the likelihood is at least $L_{min}$}
\end{itemize}
\end{itemize}

@@ -559,7 +562,9 @@ \subsection{The output is written on screen, which I forgot to save. Can
you various options to fill in. You can also run it from the command
line on OS X or Linux using

\lstinline!/path/to/beast/bin/applauncher NSLogAnalyser -N 1 -log xyz.log!
\begin{lstlisting}
/path/to/beast/bin/applauncher NSLogAnalyser -N 1 -log xyz.log
\end{lstlisting}

where the argument after \lstinline!N! is the \lstinline!particleCount!
you specified in the XML, and \lstinline!xyz.log! the trace log produced
@@ -603,7 +608,7 @@ \section{Useful Links}\label{useful-links}
\url{https://github.com/BEAST2-Dev/nested-sampling}
\item
Join the BEAST user discussion:
\url{http://groups.google.com/group/beast-users} \clearpage
\url{http://groups.google.com/group/beast-users}
\end{itemize}


@@ -624,7 +629,7 @@ \section{Useful Links}\label{useful-links}



\newpage
%\newpage

%%%%%%%%%%%%%%%%
% REFERENCES %

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