From: W. Trevor King <wking@tremily.us>
Date: Sat, 18 May 2013 03:06:41 +0000 (-0400)
Subject: sawsim/discussion.tex: Add D_JS, D_KL, p_m, ... to the nomenclature
X-Git-Tag: v1.0~172
X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=8fac547fbe2e624fccd4173242cf664b445811a1;p=thesis.git

sawsim/discussion.tex: Add D_JS, D_KL, p_m, ... to the nomenclature

Thanks Mom!

Also:
* Add chi-squared and D_chi-squared to the nomenclature
* Fix hyphen -> en-dash in Kullback--Leibler
* Label eq:sawsim:p_m (so it can be referenced from the index)
* Fix UTF-8 chi -> \chi
* Remove a dangling close-paren from eq:sawsim:X2
* Cite NIST for the chi-square comparison
* Break Gumbel and chi-squared citations into @inbook
* Add editors for the new NIST:ESH book entry
---

diff --git a/src/root.bib b/src/root.bib
index fce2aff..19e6e3c 100644
--- a/src/root.bib
+++ b/src/root.bib
@@ -219,6 +219,7 @@
 @string{MCoyne = "Coyne, M."}
 @string{DCraig = "Craig, David"}
 @string{ACravchik = "Cravchik, A."}
+@string{CCroarkin = "Croarkin, Carroll"}
 @string{VCroquette = "Croquette, Vincent"}
 @string{YCui = "Cui, Y."}
 @string{COSB = "Current Opinion in Structural Biology"}
@@ -1001,6 +1002,7 @@
 @string{NNTint = "Tint, N. N."}
 @string{BTiribilli = "Tiribilli, Bruno"}
 @string{TTlusty = "Tlusty, Tsvi"}
+@string{PTobias = "Tobias, Paul"}
 @string{JTocaHerrera = "Toca-Herrera, Jose L."}
 @string{CATovey = "Tovey, Craig A."}
 @string{AToyoda = "Toyoda, A."}
@@ -1153,18 +1155,38 @@
 @string{PGdeGennes = "de Gennes, P. G."}
 @string{PJdeJong = "de Jong, P. J."}
 @string{NGvanKampen = "van Kampen, N.G."}
-@string{NISTSEMATECH = "{NIST/SEMATECH}"}
+@string{NIST:SEMATECH = "{NIST/SEMATECH}"}
 @string{EDCola = "{\uppercase{d}}i Cola, Emanuela"}
 
-@misc { NIST:gumbel,
-    author = NISTSEMATECH,
-    key = "NIST:gumbel",
-    title = "e-Handbook of Statistical Methods: Extreme Value Type {I}
-        Distribution",
-    year = 2009,
-    month = oct,
-    day = 9,
-    url = "http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm"
+@inbook{ NIST:chi-square,
+  crossref = {NIST:ESH},
+  chapter = {1.3.5.15: Chi-Square Goodness-of-Fit Test},
+  year = 2013,
+  month = may,
+  day = 15,
+  url = {http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm},
+}
+
+@inbook{ NIST:gumbel,
+  crossref = {NIST:ESH},
+  chapter = {1.3.6.6.16: Extreme Value Type {I} Distribution},
+  year = 2009,
+  month = oct,
+  day = 9,
+  url = {http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm},
+}
+
+@book{ NIST:ESH,
+  editor = CCroarkin #" and "# PTobias,
+  author = NIST:SEMATECH,
+  title = {e-Handbook of Statistical Methods},
+  year = 2013,
+  month = may,
+  publisher = NIST:SEMATECH,
+  address = {Boulder, Colorado},
+  url = {http://www.itl.nist.gov/div898/handbook/},
+  note = {This manual was developed from seed material produced by
+    Mary Natrella.},
 }
 
 @misc{ wikipedia:gumbel,
diff --git a/src/sawsim/discussion.tex b/src/sawsim/discussion.tex
index 2a4b6e1..4e8ecd9 100644
--- a/src/sawsim/discussion.tex
+++ b/src/sawsim/discussion.tex
@@ -402,7 +402,7 @@ the similarity between two probability distributions.
 \end{equation}
 where $p_e(i)$ and $p_s(i)$ are the the values of the $i^\text{th}$
 bin in the experimental and simulated unfolding force histograms,
-respectively.  $D_\text{KL}$ is the Kullback-Leibler divergence
+respectively.  $D_\text{KL}$ is the Kullback--Leibler divergence
 \begin{equation}
   D_\text{KL}(p_p,p_q)
     = \sum_i p_p(i) \log_2\p({\frac{p_p(i)}{p_q(i)}}) \;,  \label{eq:sawsim:D_KL}
@@ -410,8 +410,16 @@ respectively.  $D_\text{KL}$ is the Kullback-Leibler divergence
 where the sum is over all unfolding force histogram bins.  $p_m$ is
 the symmetrized probability distribution
 \begin{equation}
-  p_m(i) \equiv [p_e(i)+p_s(i)]/2 \;.
+  p_m(i) \equiv [p_e(i)+p_s(i)]/2 \;.  \label{eq:sawsim:p_m}
 \end{equation}
+%
+\nomenclature{$D_\text{JS}$}{The Jensen--Shannon divergence
+  (\cref{eq:sawsim:D_JS}).}
+\nomenclature{$D_\text{LK}$}{The Kullback--Leibler divergence
+  (\cref{eq:sawsim:D_KL}).}
+\nomenclature{$p_m(i)$}{The symmetrized probability distribution used
+  in calculating the Jensen--Shannon divergence
+  (\cref{eq:sawsim:D_JS,eq:sawsim:p_m}).}
 % DONE: Mention inter-histogram normalization? no.
 %  For experiments carried out over a series of pulling velocities, we
 %  simply sum residuals computed for each velocity, although it would
@@ -421,11 +429,15 @@ the symmetrized probability distribution
 The major advantage of the Jensen--Shannon divergence is that
 $D_\text{JS}$ is bounded ($0\le D_\text{JS}\le 1$) regardless of the
 experimental and simulated histograms.  For comparison, Pearson's
-$\chi^2$ test,
+$\chi^2$ test\citep{NIST:chi-square},
 \begin{equation}
-  D_{χ^2} = \sum_i \frac{(p_e(i)-p_s(i))^2}{p_s(i)}) \;,  \label{eq:sawsim:X2}
+  D_{\chi^2} = \sum_i \frac{(p_e(i)-p_s(i))^2}{p_s(i)} \;,
+  \label{eq:sawsim:X2}
 \end{equation}
 is infinite if there is a bin for which $p_e(i)>0$ but $p_s(i)=0$.
+%
+\nomenclature{$\chi^2$}{The chi-squared distribution}
+\nomenclature{$D_{\chi^2}$}{Pearson's $\chi^2$ test (\cref{eq:sawsim:X2}).}
 
 \Cref{fig:sawsim:fit-space} shows the Jensen--Shannon divergence
 calculated using \cref{eq:sawsim:D_JS} between an experimental data