So much issue closing...

1: fixing hard spaces (regex: \\\(.*\)\~/\\\1\\\ /g
2: getting rid of all e.g.s
3: also had to fix use of \pr (what) vs. \pr{what}

document/doc.tex

@@ -144,17 +144,17 @@
 
     We introduce a stable, well tested Python implementation of the affine-%
     invariant ensemble sampler for Markov chain Monte Carlo (MCMC)
-    proposed by Goodman~\&~Weare (2010). The code is open source and has
+    proposed by Goodman \& Weare (2010). The code is open source and has
     already been used in several published projects in the Astrophysics
-    literature. The algorithm behind \this~has several advantages over
+    literature. The algorithm behind \this\ has several advantages over
     traditional MCMC sampling methods and it has excellent performance as
     measured by the autocorrelation time.
     One major advantage of the algorithm is that it requires hand-tuning of
     only 2 parameters compared to $\sim N^2$ for
     a traditional algorithm in an $N$-dimensional parameter space. In this
     \paper, we describe the algorithm and the details of our implementation
     and API. Taking advantage of the naturally parallel nature of
-    the algorithm, \this~permits \emph{any} user to take advantage of
+    the algorithm, \this\ permits \emph{any} user to take advantage of
     multiple CPUs without extra effort. This is a huge advantage over a
     na\"ive implementation of the published algorithm when applied to
     computationally expensive problems.
@@ -191,7 +191,7 @@ \section{Introduction}
 parameter spaces. This has proved useful in too many research
 applications to list here but the results from the Wilkinson Microwave
 Anisotropy Probe (WMAP) mission provide a dramatic example
-\citep[e.g.][]{Dunkley:2005}.
+\citep[for example][]{Dunkley:2005}.
 
 Arguably the most important advantage of Bayesian data analysis is
 that it is possible to \emph{marginalize} over nuisance parameters. A
@@ -226,7 +226,8 @@ \section{Introduction}
 
 Most uses of MCMC in the astrophysics literature are based on slight
 modifications to the Metropolis-Hastings (M-H) method
-\citep[e.g.][]{MacKay:2003}. Each step in a M-H chain is proposed using a
+\citep[for example][]{MacKay:2003}. Each step in a M-H chain is proposed
+using a
 multivariate Gaussian centered on the current position of the chain. Since
 each term in the covariance matrix of this proposal distribution is an
 unspecified parameter, this method has $N\,[N+1]/2$ tuning parameters (where
@@ -235,8 +236,8 @@ \section{Introduction}
 tuning parameters and there is no fool-proof method for choosing the values
 correctly. As a result, many heuristic methods have been developed to attempt
 to determine the optimal parameters in a data-driven way
-\citep[e.g.][]{Gregory:2005,Dunkley:2005,Widrow:2008}. Unfortunately, these
-methods all require ``burn-in'' phases where shorter Markov chains
+\citep[for example][]{Gregory:2005,Dunkley:2005,Widrow:2008}. Unfortunately,
+these methods all require ``burn-in'' phases where shorter Markov chains
 are sampled and the results are used to tune the hyperparameters. This extra
 cost is unacceptable when the likelihood calls are computationally heavy.
 
@@ -273,7 +274,7 @@ \section{Introduction}
 performance. \citet{Hou:2011} were the first group to implement this
 algorithm to solve a physics problem. The implementation presented here is
 an independent effort that has already proved effective in several projects
-\citep[][Foreman-Mackey \& Widrow~2012, in prep.]{Lang:2011,
+\citep[][Foreman-Mackey \& Widrow\ 2012, in prep.]{Lang:2011,
 Bovy:2011, Dorman:2012}.
 In what follows, we summarize the GW algorithm and the implementation
 decisions made in \this. We also describe the small changes
@@ -290,31 +291,31 @@ \section{The Algorithm}\sectlabel{algo}
 $\{ \model_i \, \forall i=1, \ldots, M \}$ from
 the joint probability distribution
 \begin{equation}
-    \pr (\model, \nuisance, \data) = \pr (\model, \nuisance)
+    \pr{\model, \nuisance, \data} = \pr{\model, \nuisance}
             \, \pr (\data | \model, \nuisance)
 \end{equation}
-where the prior distribution $\pr (\model, \nuisance)$ and the likelihood
-function $\pr (\data|\model,\nuisance)$ can be relatively easily (but not
+where the prior distribution $\pr{\model, \nuisance}$ and the likelihood
+function $\pr{\data|\model,\nuisance}$ can be relatively easily (but not
 necessarily quickly) computed for a particular value of
-$(\model_i, \nuisance_i)$. Since the normalization $\pr (\data)$ is
+$(\model_i, \nuisance_i)$. Since the normalization $\pr{\data}$ is
 independent of $\model$ and $\nuisance$, the joint distribution above is
-proportional to the posterior probability $\pr (\model, \nuisance | \data)$
+proportional to the posterior probability $\pr{\model, \nuisance | \data}$
 given any one choice of generative model. Therefore, once the samples
 produced by MCMC are available, the marginalized constraints on $\model$
 (\eq{marginalization}) can be approximated by the histogram of the samples
 projected into the subspace spanned by $\model$. In particular, the
 expectation value of a particular parameter $\phi \in \model$ given the
 samples $\{ \phi_i \}$ is
 \begin{equation}
-    E[\phi] = \int \phi \, \pr ( \model, \nuisance | \data )
+    E[\phi] = \int \phi \, \pr{\model, \nuisance | \data}
             \, \dd \model \, \dd \nuisance
             \approx \frac{1}{M} \sum_{i=1} ^M \phi_i .
 \end{equation}
 Generating the samples $\model_i$ is a non-trivial process unless
-$\pr (\model, \nuisance, \data)$ is a very specific analytic distribution
-(e.g.~Gaussian). MCMC is a procedure for generating a random walk in the
-parameter space the relatively efficiently draws a representative set of
-samples from the distribution. Each point in a Markov chain
+$\pr{\model, \nuisance, \data}$ is a very specific analytic distribution
+(for example, a Gaussian). MCMC is a procedure for generating a random walk
+in the parameter space the relatively efficiently draws a representative set
+of samples from the distribution. Each point in a Markov chain
 $\link (t) = [\model(t), \nuisance(t)]$
 depends only on the position of the previous link $\link (t-1)$.
 
@@ -326,11 +327,11 @@ \section{The Algorithm}\sectlabel{algo}
 $Q(Y; X(t))$, (2) accept this proposal with probability
 \begin{equation}
     \mathrm{min} \left \{ 1,
-            \frac{\pr(\vector{Y} | \data)}{\pr(\vector{X}(t) | \data)} \,
+            \frac{\pr{\vector{Y} | \data}}{\pr{\vector{X}(t) | \data}} \,
             \frac{Q(X(t); Y)}{ Q(Y;X(t))}  \right \}.
 \end{equation}
 It is worth emphasizing that if this step is accepted $X(t+1) = Y$; Otherwise,
-the new position is set to the previous one $X(t+1) \gets X(t)$ (i.e.~the
+the new position is set to the previous one $X(t+1) \gets X(t)$ (i.e.\ the
 position $X(t)$ is \emph{double counted}).
 
 The M-H algorithm converges (as $t \to \infty$) to a stationary set of
@@ -351,8 +352,8 @@ \section{The Algorithm}\sectlabel{algo}
 \begin{algorithmic}[1]
 
 \STATE Draw a sample $Y \sim Q (Y; X(t))$
-\STATE $q \gets [\pr(\vector{Y}) \, Q(X(t); Y)]
-        / [\pr(\vector{X}(t)) \, Q(Y;X(t))]$
+\STATE $q \gets [\pr{\vector{Y}} \, Q(X(t); Y)]
+        / [\pr{\vector{X}(t)} \, Q(Y;X(t))]$
 \STATE $r \gets R \sim [0, 1]$
 \IF{$r \ge q$}
     \STATE $\vector{X}(t+1) \gets \vector{Y}$
@@ -395,7 +396,7 @@ \section{The Algorithm}\sectlabel{algo}
 \begin{equation}
     \eqlabel{acceptance}
     q = \min \left \{ 1, Z^{n-1} \,
-                \frac{\pr(\vector{Y})}{\pr(\vector{X_k} (t))} \right \}
+                \frac{\pr{\vector{Y}}}{\pr{\vector{X_k} (t)}} \right \}
 \end{equation}
 where $n$ is the dimension of the parameter space. This procedure is then
 repeated for each walker in the ensemble \emph{in series} following the
@@ -524,7 +525,7 @@ \section{Benchmarks \& Tests} \sectlabel{tests}
     \tau = \sum_{t= -\infty} ^{\infty} \frac{C(t)}{C(0)} .
 \end{equation}
 
-\this~can optionally calculate the autocorrelation time using the Python
+\this\ can optionally calculate the autocorrelation time using the Python
 module \project{acor}\footnote{\url{http://github.com/dfm/acor}} to estimate
 the autocorrelation time. This module is a direct port of the original
 algorithm \citepalias[described by][]{Goodman:2010} and implemented by those
@@ -550,7 +551,8 @@ \section{Benchmarks \& Tests} \sectlabel{tests}
 
 \section{Discussion \& Tips}
 
-% DFM: In this section, I put the key advice from each paragraph in \emph{}.  Hogg
+% DFM: In this section, I put the key advice from each paragraph in
+% \emph{}.  Hogg
 
 The goal of this project has been to make a sampler that is a useful
 tool for a large class of data analysis problems---a ``hammer'' if you
@@ -661,7 +663,7 @@ \section{Discussion \& Tips}
 \begin{thebibliography}{}
 \raggedright
 
-\bibitem[Bovy~\etal(2011)]{Bovy:2011}
+\bibitem[Bovy\ \etal(2011)]{Bovy:2011}
  Bovy,~J., Rix,~H.-W., Liu,~C., Hogg,~D.~W., Beers,~T.~C., \& Lee,
 Y.~S., 2011, \apj, submitted, arXiv:1111.1724 [astro-ph.GA]
 % http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1111.1724
@@ -670,21 +672,21 @@ \section{Discussion \& Tips}
 {Christen}, J., \emph{A general purpose scale-independent MCMC algorithm},
 technical report I-07-16, CIMAT, Guanajuato, 2007.
 
-\bibitem[Dorman~\etal(2012)]{Dorman:2012}
+\bibitem[Dorman\ \etal(2012)]{Dorman:2012}
 {Dorman},~C., {Guhathakurta},~P., {Fardal},~M.~A., {Geha},~M.~C.,
 {Howley},~K.~M., {Kalirai},~J.~S., {Lang},~D., {Cuillandre}, J.,
 {Dalcanton},~J., {Gilbert},~K.~M., {Seth},~A.~C., {Williams},~B.~F.,
-\& {Yniguez},~B., 2012, \apj, submitted
+\& {Yniguez},\ B., 2012, \apj, submitted
 % http://adsabs.harvard.edu/abs/2012AAS...21934608D
 
-\bibitem[Dunkley~\etal(2005)]{Dunkley:2005}
+\bibitem[Dunkley\ \etal(2005)]{Dunkley:2005}
 {Dunkley}, J., {Bucher}, M., {Ferreira}, P.~G., {Moodley}, K.,
 \& {Skordis}, C.,
 2005, \mnras, 356, 925-936
 % http://adsabs.harvard.edu/abs/2005MNRAS.356..925D
 
-\bibitem[Goodman~\&~Weare(2010)]{Goodman:2010}
-Goodman,~J., \& Weare,~J.,
+\bibitem[Goodman~\&\ Weare(2010)]{Goodman:2010}
+Goodman,~J., \& Weare,\ J.,
 2010, Comm.\ App.\ Math.\ Comp.\ Sci., 5, 65
 
 \bibitem[Gregory(2005))]{Gregory:2005}
@@ -693,12 +695,12 @@ \section{Discussion \& Tips}
 Cambridge University Press, 2005
 % http://adsabs.harvard.edu/abs/2005blda.book.....G
 
-\bibitem[Hou~\etal(2011))]{Hou:2011}
+\bibitem[Hou\ \etal(2011))]{Hou:2011}
 {Hou}, F., {Goodman}, J., {Hogg}, D.~W., {Weare}, J., \& {Schwab}, C.,
 2011, arXiv:1104.2612
 % http://adsabs.harvard.edu/abs/2011arXiv1104.2612H
 
-\bibitem[Lang~\& Hogg(2011))]{Lang:2011}
+\bibitem[Lang\ \& Hogg(2011))]{Lang:2011}
 {Lang}, D. and {Hogg}, D.~W.,
 2011, arXiv:1103.6038
 % http://adsabs.harvard.edu/abs/2011arXiv1103.6038L
@@ -707,7 +709,7 @@ \section{Discussion \& Tips}
 {MacKay}, D., \emph{Information Theory, Inference, and Learning Algorithms},
 Cambridge University Press, 2003
 
-\bibitem[Widrow~\etal(2008))]{Widrow:2008}
+\bibitem[Widrow\ \etal(2008))]{Widrow:2008}
 {Widrow}, L.~M. and {Pym}, B. and {Dubinski}, J.,
 2008, \apj, 679, 1239
 % http://adsabs.harvard.edu/abs/2008ApJ...679.1239W
@@ -720,17 +722,17 @@ \section{Usage}\sectlabel{api}
 
 \paragraph{Installation}
 
-The easiest way to install \this~is using
+The easiest way to install \this\ is using
 \pip\footnote{\url{http://pypi.python.org/pypi/pip/}}. Running the command
 \begin{lstlisting}
 % pip install emcee
 \end{lstlisting}
 at the command line of a UNIX-based system will install the package and its
-\Python~dependencies. If you would like to install for all users, you might
-need to run the above command with superuser permissions. \this~depends on
-\Python~($>2.7$) and \numpy\footnote{\url{http://numpy.scipy.org}} ($>1.6$)
+\Python\ dependencies. If you would like to install for all users, you might
+need to run the above command with superuser permissions. \this\ depends on
+\Python\ ($>2.7$) and \numpy\footnote{\url{http://numpy.scipy.org}} ($>1.6$)
 and the associated \texttt{dev} headers. On some systems, you might need to
-install these packages separately. On most systems where \Python~has already
+install these packages separately. On most systems where \Python\ has already
 been installed, this won't be necessary but if it is, you can install
 dependencies (on \Ubuntu, for example) with the command:
 \begin{lstlisting}
@@ -742,12 +744,12 @@ \section{Usage}\sectlabel{api}
 \begin{lstlisting}
 % python setup.py install
 \end{lstlisting}
-in the unzipped directory. Make sure that you have \numpy~installed in this
+in the unzipped directory. Make sure that you have \numpy\ installed in this
 case as well.
 
 \paragraph{Issues \& Contributions}
 
-The development of \this~is being coordinated on \github~at
+The development of \this\ is being coordinated on \github\ at
 \url{http://github.com/dfm/emcee} and contributions are welcome. If you
 encounter any problems with the code, please report them at
 \url{http://github.com/dfm/emcee/issues} (DFM: check this url) and consider
@@ -758,7 +760,7 @@ \section{Usage}\sectlabel{api}
 A very simple sample problem and a common unit test for sampling code is
 the performance of the code on a high dimensional Gaussian density
 \begin{equation}\eqlabel{mgauss}
-    \pr (\mathbf{x}) \propto \exp\left ( -\frac{1}{2} \mathbf{x}^T \,
+    \pr{\mathbf{x}} \propto \exp\left ( -\frac{1}{2} \mathbf{x}^T \,
                                 \Sigma^{-1} \, \mathbf{x} \right ).
 \end{equation}
 We will incrementally work through this example here and the source code