BSTA 670 – Statistical Computing

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BSTA 670 – Statistical Computing. Lecture 4, Extra Material: A Brief Introduction to LaTeX. What are TeX and LaTeX?. TeX (tau epsilon chi) is a computer language designed for typesetting, especially math.

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BSTA 670 – Statistical Computing

Lecture 4, Extra Material:

A Brief Introduction to LaTeX

What are TeX and LaTeX?
• TeX (tau epsilon chi) is a computer language designed for typesetting, especially math.
• TeX was developed by Donald Knuth, a Mathematician/Computer Scientist, and others in late 1970s. He was dissatisfied with the typesetting from the publisher of his book “The Art of Computer Programming”. The development took about 10 years.
• TeX is an interpreter language, accepting commands based on markup language, written in ascii files.
What are TeX and LaTeX?
• TeX is portable, producing the same output on any computer.
• TeX is a very low level language directing where and what to place on a page. For example: move a specific distance to the left, right, up, or down ; change font; write a string of words, possibly containing math expressions, to a paragraph, etc.
What are TeX and LaTeX?
• TeX processes the input commands and produces a device independent file (dvi). This file then gets translated for the particular output device; screen, pdf, postscript (.ps).
• TeX requires a set of fonts. Donald Knuth also developed a font creation program called Metafont. All TeX installations have a basic set of fonts, other fonts can be generated or added, included commercially available fonts.
What are TeX and LaTeX?
• Macro commands can be defined to build the low level commands into high level command interfaces. For example, a macro to create a title page and to set up sections and subsections, etc.
• LaTeX is a variation of TeX that is easier to use than basic TeX. It is essentially a macro package that runs using TeX. The macros provide many useful features including the ability to create documents with sections and chapters, bibliography macros.
What are TeX and LaTeX?
• Essentially, LaTeX provides easier document style implementation, while also providing the ease of math typesetting.
• LaTeX also provides the ability to include graphics in documents, although in some implementations of LaTeX it is not easy to do so.
• LaTeX style files have been created to format common document features, such as paragraphing, margins, footnotes, headers, etc.
What are TeX and LaTeX?
• LaTeX style files include: letter, book, article, and report.
• A style file can be written for any use such as for formatting a Ph.D. thesis. The thesis formats for Penn are available at: http://www.math.upenn.edu/grad/thesisstyle.html
• TeX/LaTeX is available for Windows, Unix, Linux, and Mac OS. It can be obtained for free or commercially.
What are TeX and LaTeX?
• The Comprehensive TeX Archive Network (CTAN) is the most comprehensive site. http://www.ctan.org/
• Some info on LaTeX: http://www.latex-project.org/
• Free versions include: Windows (proTeXt, MiKTeX), Unix/Linux (TeX Live), Mac (gwTeX). There are many others.
• Commercial versions: Windows (PCTeX, TurboTeX), Mac (Textures).
What are TeX and LaTeX?
• TeX is not WYSIWYG (What you see is what you get).
• MS WORD and WordPerfect are WYSIWYG.
• In WYSIWYG text processors: what you see on the screen as you edit is the final product, formatting commands are not visible.
• LaTex and Tex are not word processors. Rather, they are text formatters. The formatting commands are visible (in a command file). The command file defines the structure of the final product and a compiler is needed to process the commands.

LaTeX

• LaTeX has two modes for the typed characters: Math Mode and Text Mode. The mode determines how LaTeX responds to the entered text.
• Default is text mode.
• Math mode is indicated by surrounded the math phrase with a $on each end, e.g.$\alpha$. The math symbol \alpha will only work in math mode. LaTeX document layout \documentclass{class} \begin{document} .... your text goes here .... \end{document} Class can be article (publication article), report (document with chapters), letter, book. Example of LaTeX Input and Output \documentclass{article} \begin{document} This is a simple example of the use of \LaTeX{}. Files must contain special commands that declare the \emph{document class}, most often article’’, and that denote the beginning and end of the document itself, \emph{begin} and \emph{end}. The \emph{preamble} is the initial part of the file, between the document class command and the beginning of the document. This may contain commands specifying font information, defintion of new commands, author and title information, or other commands. The text of the document goes between the begin and end commands. Paragraphs are indicated by blank lines. Segments of the text that are to printed in \textbf{boldface} {\bf font}, {\it italics}, or \underline{underlined} are simply surrounded by the appropriate \emph{environment}. \end{document} simple.tex Font Sizes \documentclass[12pt]{article} \begin{document} There are various font sizes that can be accessed. Others can be created in needed. {\tiny tiny} \\ {\scriptsize scriptsize} \\ {\footnotesize footnotesize} \\ {\small small} \\ {\normalsize normalsize} \\ {\large large} \\ {\Large Large} \\ {\LARGE LARGE} \\ {\huge huge} \\ {\Huge Huge} \end{document} font_sizes.tex Font Sizes \documentclass[12pt]{article} \begin{document} \LARGE You can easily change {\normalsize from} one font {\huge to another font size}. This \small can be done {\footnotesize for a specific set of text} or from \large a specific point onward. \end{document} font_sizes2.tex Formatting in LaTeX • Sections • \section{…} = 1. This is section • \subsection{…} = 1.1 This is subsection • \subsubsection{…} = 1.1.1 This is subsubsection • \appendix - changes to numbering for appendix • \chapter{…} - Used with book and report documents • Title page: • \title{…} • \author{…} • \maketitle - Display Title and Author Formatting in LaTeX • \tableofcontents - Creates TOC • \listoftables - Creates LOT • \listoffigures - Creates LOF • \label{marker} – Marker for object in document. • \pageref{marker} - Displays page no. of marker. • \ref{marker} - Displays section location of marker. Example 1 of Article in LaTeX \documentclass[titlepage]{article} \begin{document} \title{Article Example} \author{Joe First} \date{November xx, 2008} \maketitle \section{INTRODUCTION} \label{intro} This is the introduction section. \section{NOTATION AND METHODS} \label{methods} Let$N_0$, and$N_1$be the numbers of unexposed and exposed members of the population, respectively, and let other quantities be defined as in Table 1. We are interested in$p_0$= P(true disease$|$unexposed) and$p_1$= P(true disease$|$exposed). Usual risk measures such as the risk difference$p_1 - p_0$or relative risk$p_1/p_0$can be based on estimates of$p_0$and$p_1$. \end{document} article_ex1.tex Example 1 of Math in LaTeX \documentclass[12pt]{article} \begin{document} Suppose X represents the lifetime random variable and T the truncation random variable for Group~1 and Y represents the lifetime random variable and Z the truncation random variable for Group~2. Also, suppose that X, Y, T, and Z are all independent. The pair$(X,T)$is observed if and only if$X \leq T$and the pair$(Y,Z)$is observed if and only if$Y \leq Z$. Under this sampling scheme, only the pairs in Group~1 satisfying$x_i \leq t_i$, denoted$(x_1, t_1), \ldots, (x_{n_1}, t_{n_1})$, are observed. Also, only the pairs in Group~2 satisfying$y_j \leq z_j$, denoted$(y_1, z_1), \ldots, (y_{n_2}, z_{n_2})$, are observed. \end{document} math_ex1.tex \documentclass[12pt]{article} \begin{document} Here is an equation with a label for referencing the equation number. \label{areform} ARE \doteq 1- \frac{ \pi_0 k + \pi_1 - \pi_0 \pi_1 \left( (1-f_0) +k(1-f_1) \right) - \pi_1 f_0 - \pi_0 f_1 k } { \pi_0 k + \pi_1 - \pi_0 \pi_1 \left( (1-f_0) +k(1-f_1) \right) \hspace{1.15in} }. By definition,$k=f_0 T_0 / f_1 T_1$which yields$T_0 = (f_1 T_1 k)/f_0$. Substituting this result into$f$yields$f= f_0 f_1 (k+1) / (f_1 k + f_0)$. The ARE comparing full verification to the BG method is obtained by substituting$f_0=f_1=f$into Equation~\ref{areform}. \end{document} Example 2 of Math in LaTeX \documentclass[12pt]{article} \begin{document} Here is an equation with a label for referencing the equation number. \label{areform} ARE \doteq 1- \frac{ \pi_0 k + \pi_1 - \pi_0 \pi_1 \left( (1-f_0) +k(1-f_1) \right) - \pi_1 f_0 - \pi_0 f_1 k } { \pi_0 k + \pi_1 - \pi_0 \pi_1 \left( (1-f_0) +k(1-f_1) \right) \hspace{1.15in} }. By definition,$k=f_0 T_0 / f_1 T_1$which yields$T_0 = (f_1 T_1 k)/f_0$. Substituting this result into$f$yields$f= f_0 f_1 (k+1) / (f_1 k + f_0)$. The ARE comparing full verification to the BG method is obtained by substituting$f_0=f_1=f$into Equation~\ref{areform}. \end{document} math_ex2.tex \documentclass[12pt]{article} \begin{document} Here is an equation with a label for referencing the equation number. \label{areform} ARE \doteq 1- \frac{ \pi_0 k + \pi_1 - \pi_0 \pi_1 \left( (1-f_0) +k(1-f_1) \right) - \pi_1 f_0 - \pi_0 f_1 k } { \pi_0 k + \pi_1 - \pi_0 \pi_1 \left( (1-f_0) +k(1-f_1) \right) \hspace{1.15in} }. By definition,$k=f_0 T_0 / f_1 T_1$which yields$T_0 = (f_1 T_1 k)/f_0$. Substituting this result into$f$yields$f= f_0 f_1 (k+1) / (f_1 k + f_0)$. The ARE comparing full verification to the BG method is obtained by substituting$f_0=f_1=f$into Equation~\ref{areform}. \end{document} \documentclass[12pt]{article} \begin{document} The construction of the Mann-Whitney statistic is based on information of the patterns found in the ordered combined sample. Define \begin{displaymath} U_{ij} = U(X_i,Y_j) = \left\{ \begin{array}{lr} {+1} & \hspace{2ex} X_i > Y_j \\ { 0} & \hspace{2ex} X_i = Y_j \\ {-1} & \hspace{2ex} X_i < Y_j \end{array} \right. \end{displaymath} The Mann-Whitney statistic is defined as \begin{displaymath} U = \frac{1}{n_1 n_2} \sum_{i=1}^{n_1}\sum_{j=1}^{n_2} U_{ij} \end{displaymath} The Mann-Whitney statistic,$U$, and Wilcoxon statistic,$W$, can be shown to be related according to$ W = 2^{-1} \left[ n_1 n_2 U + n_1(n_1+n_2+1) \right] $. It should be noted here that the Mann-Whitney statistic is sometimes defined with$U_{ij}$being an indicator function taking on values 1 if$X_i>Y_j$and 0 otherwise. Exact moments for the Wilcoxon statistic can be derived through the use of permutation theory. \end{document Example 3 of Math in LaTeX math_ex3.tex \documentclass[12pt]{article} \begin{document} Here is an equation with a label for referencing the equation number. \label{areform} ARE \doteq 1- \frac{ \pi_0 k + \pi_1 - \pi_0 \pi_1 \left( (1-f_0) +k(1-f_1) \right) - \pi_1 f_0 - \pi_0 f_1 k } { \pi_0 k + \pi_1 - \pi_0 \pi_1 \left( (1-f_0) +k(1-f_1) \right) \hspace{1.15in} }. By definition,$k=f_0 T_0 / f_1 T_1$which yields$T_0 = (f_1 T_1 k)/f_0$. Substituting this result into$f$yields$f= f_0 f_1 (k+1) / (f_1 k + f_0)$. The ARE comparing full verification to the BG method is obtained by substituting$f_0=f_1=f$into Equation~\ref{areform}. \end{document} Example 3 of Math in LaTeX math_ex3.tex Example 4 of Math in LaTeX \documentclass[12pt]{article} \begin{document} \begin{displaymath} \begin{array}{cccc} \underline{Age Group At} & \underline{Sample Size} & \underline{Truncation MW} & \underline{Weighted LR} \\ \underline{First Transfusion}& & \underline{Statistic} & \underline{Statistic} \\ & & & \\ 13-29 \hspace{1ex} years & 188 & Z=1.80 & Z=-1.39 \\ 40-49 \hspace{1ex} years & 148 & P=0.072 & P=0.166 \\ & & & \\ 13-29 \hspace{1ex} years & 188 & Z=2.62 & Z=-3.45 \\ 70+ \hspace{1ex} years & 115 & P=0.009 & P<0.001 \\ & & & \\ 40-49 \hspace{1ex} years & 148 & Z=2.73 & Z=-2.61 \\ 70+ \hspace{1ex} years & 115 & P=0.006 & P=0.009 \end{array} \end{displaymath} \end{document} math_ex4.tex Example 5 of Math in LaTeX \documentclass[12pt]{article} %\def\jot{8mm} % set interrow space for equations in eqnarray, etc. Default is 3pt = 0.0415 in = 0.1054 mm. \newdimen\jot \jot=4mm % This command has exactly the same effect as the \def command above. It is used in the % latex setup file in /usr/local/lib/tex/inputs. Also, unlike \def, it can be used throughout the document to change % the value of jot at any time. \newcommand{\piah}{\mbox{$\hat{\pi}_0$}} % staru is used for placing a superscript star slightly higher than TeX normally places it. It is used in places where a % star is placed on a capital letter (R and K) since TeX doesn\'t place it high enough for my taste. The hspace is % required since a space is added after the star. The -1ex hspace removes this space. \newcommand{\staru}{\raisebox{.6ex}{$\scriptsize\star$}\hspace{-1ex}} \newcommand{\pas}{\mbox{$p_0^{\staru\ }$}} \newcommand{\pahs}{\mbox{$\hat{p}_0^{\staru\ }$}} \begin{document} It is now shown that$\pahs\ =T_0/N_0$and$\piah\ =X_0/M_0$are uncorrelated. The conditional covariance$Cov(\pahs\ , \piah\ | D_0, W_0) = 0$, because$T_0=D_0+W_0$. Therefore, \noindent \begin{eqnarray*} Cov(\pahs\ , \piah\ ) & = & E \left[ 0 \right] + Cov \left[ E \left( \pahs\ | D_0, W_0 \right), E \left( \piah\ | D_0, W_0 \right) \right] \nonumber \\ & = & Cov \left[ \frac{T_0}{N_0}, \frac{D_0}{D_0+W_0} \right] \nonumber \\ & = & E \left( \frac{D_0}{N_0} \right) - E \left( \frac{T_0}{N_0} \right) E \left( \frac{D_0}{D_0+W_0} \right) \nonumber \\ & = & p_0 - \pas\ \pi_0 = 0. \end{eqnarray*} \end{document} math_ex5.tex Example 6 of Math in LaTeX \documentclass[12pt]{article} \begin{document} Table~\ref{tabcomp} shows the ARE comparing the BBGS and BG methods. \begin{table}[htbp] \caption{Examples of ARE Comparing BBGS and BG Methods} \label{tabcomp} \begin{center} \begin{tabular}[h]{|c|c||c|c||c|c|} \hline \hline \multicolumn{2}{|c||}{$T_0 = 500$,$T_1=25$} & \multicolumn{2}{|c||}{$T_0 = 500$,$T_1=50$} & \multicolumn{2}{|c| }{$T_0 = 500$,$T_1=100$} \\ \multicolumn{2}{|c||}{$\pi_0=0.7$,$f_0=0.3$} & \multicolumn{2}{|c||}{$\pi_0=0.6$,$f_0=0.3$} & \multicolumn{2}{|c| }{$\pi_0=0.5$,$f_0=0.3$} \\ \multicolumn{2}{|c||}{$k=6$} & \multicolumn{2}{|c||}{$k=3$} & \multicolumn{2}{|c| }{$k=1.5$} \\ \hline$\pi_1$& RE &$\pi_1$& RE &$\pi_1$& RE \\ \hline \hline 0.2 & 0.391 & 0.1 & 0.433 & 0.1 & 0.520 \\ 0.5 & 0.516 & 0.3 & 0.576 & 0.3 & 0.703 \\ 0.7 & 0.646 & 0.6 & 0.711 & 0.5 & 0.847 \\ 0.8 & 0.736 & 0.7 & 0.798 & 0.7 & 0.928 \\ 0.9 & 0.851 & 0.9 & 0.902 & 0.9 & 1.016 \\ \hline \hline \end{tabular} \end{center} \end{table} \end{document} math_ex6.tex Example 7 of Math in LaTeX \documentclass[12pt]{article} \newcommand{\staru}{\raisebox{.6ex}{$\scriptsize\star$}\hspace{-1ex}} \newcommand{\pas}{\mbox{$p_0^{\staru\ }$}} \newcommand{\pbs}{\mbox{$p_1^{\staru\ }$}} \begin{document} \begin{displaymath} \displaystyle \frac{ \displaystyle \frac{1}{p_0^2} \left[ \displaystyle \frac{\pi_0^2 \pas\ (1- \pas\ )}{N_0} + \displaystyle \frac{\pas\ \pi_0 (1- \pi_0 )}{N_0} \right] + \displaystyle \frac{1}{p_1^2} \left[ \displaystyle \frac{\pi_1^2 \pbs\ (1- \pbs\ )}{N_1} + \displaystyle \frac{\pbs\ \pi_1 (1- \pi_1 )}{N_1} \right] } { \displaystyle \frac{1}{p_0^2} \left[ \displaystyle \frac{\pi_0^2 \pas\ (1- \pas\ )}{N_0} + \displaystyle \frac{\pas\ \pi_0 (1- \pi_0 )}{f_0 N_0} \right] + \displaystyle \frac{1}{p_1^2} \left[ \displaystyle \frac{\pi_1^2 \pbs\ (1- \pbs\ )}{N_1} + \displaystyle \frac{\pbs\ \pi_1 (1- \pi_1 )}{f_1 N_1} \right] } \,\ . \end{displaymath} \end{document} math_ex7.tex Example 8 of Math in LaTeX \documentclass[12pt]{article} \def\baselinestretch{1.20} % %\def\jot{8mm} % set interrow space for equations in eqnarray, etc % default is 3pt = 0.0415 in = 0.1054 mm \newdimen\jot \jot=4mm \newcommand{\staru}{\raisebox{.6ex}{$\scriptsize\star$}\hspace{-1ex}} \newtheorem{plemmat}{Proof of Lemma} \newenvironment{plemma}{\begin{plemmat} \,\ \\ \rm}{\end{plemmat}} \newcommand{\littleops}[2]{\mbox{$ {o_{p_n}^\star}({ n^{- \frac{#1}{#2}}}) $}} \newcommand{\shn}{\mbox{${{\hat{S}}}(s)$}} \newcommand{\shsn}{\mbox{${{\hat{S}}^{\staru\ }}(s)$}} \newcommand{\khs}{\mbox{${{\hat{K}}^{\staru\ }}(u)$}} \newcommand{\khbs}{\mbox{${\hat{{\overline{K}}}^\star}\hspace{-0.5ex}(u)$}} \newcommand{\kh}{\mbox{${\hat{K}}(u)$}} \newcommand{\khb}{\mbox{${\hat{{\overline{K}}}}(u)$}} \newcommand{\rhs}{\mbox{${{\hat{R}}^{\staru\ }}(u)$}} \newcommand{\rh}{\mbox{${\hat{R}}(u)$}} \begin{document} math_ex8.tex / continued next page Example 8 of Math in LaTeX \begin{plemma} \vspace{-12pt} \begin{eqnarray*} \log \shsn\ & - & \log \shn\ = - \left[ { \int_0^s \frac{d \khs\ }{\rhs\ } } - { \int_0^s \frac{d \kh\ }{\rh\ } } \right] + \littleops{1}{2} \\ & = & \int_0^s \left( \frac{1}{\rhs\ }-\frac{1}{\rh\ } \right)d\khb\ + \int_0^s \frac{1}{\rh\ } d \left( \khbs\ - \khb\ \right) \\ & & + \int_0^s \left( \frac{1}{\rhs\ }-\frac{1}{\rh\ } \right) d \left( \khbs\ - \khb\ \right) + \littleops{1}{2} \\ & = & {\cal A} + {\cal B} + {\cal C} + \littleops{1}{2} \end{eqnarray*} \end{plemma} \end{document} math_ex8.tex / continued from last page Example of Bibtex in LaTeX \documentclass[12pt]{article} \begin{document} \bibliographystyle{unsrt} \section{INTRODUCTION} \label{intro} One of the primary methodologic concerns with population-based database studies is the potential for errors in the diagnoses reported in the database. Thus, the performance of pharmacoepidemiologic studies using these large databases usually requires verification of diagnoses reported in the database \cite{Carson1994}, which may be accomplished, for example, by obtaining medical records of the presumptive cases identified in the database. Brenner and Gefeller \cite{Brenner1993a} examined a similar design for estimating relative risks, but they used the same sampling fraction for verifying the disease status of exposed and unexposed presumptive cases. \bibliography{bibtex_ex_refs} % Refers to file: bibtex_ex_refs.bib \end{document} bibtex_ex.tex Example of Bibtex in LaTeX @ARTICLE{Brenner1993a, AUTHOR = "Brenner H and Gefeller O", TITLE = "Use of the positive predictive value to correct for disease misclassification in epidemiologic studies", YEAR = "1993", JOURNAL = "Am J Epidemiol", VOLUME = "138", PAGES = "1007-1015" } @BOOK{Carson1994, AUTHOR = "Carson JL and Strom BL", TITLE = "Medicaid databases. Chapter 15 in Strom BL: Pharmacoepidemiology", PUBLISHER = "John Wiley and Sons, Chichester", EDITION = "Second", YEAR = "1994" } bibtex_ex_refs.bib \documentclass[12pt]{article} \begin{document} \section{INTRODUCTION} \label{intro} This is section~\ref{intro}. Section~\ref{methods} will follow. \section{NOTATION AND METHODS} \label{methods} This is section~\ref{methods} , which follows section~\ref{intro}. \section{RESULTS} \label{results} This is section 3. \subsection{ARE OF METHOD FOR${\bf log(\hat{RR})}$RELATIVE TO FULL VERIFICATION} \label{arefull} This is subsection~\ref{arefull}, which is within section~\ref{results}. \subsection{ARE OF METHOD FOR${\bf log(\hat{RR})}$RELATIVE TO BG APPROACH} \label{arebg} This is subsection~\ref{arebg}, which is within section~\ref{results}. \section{CONCLUSIONS} \label{last} This is section~\ref{last}. The first section was section~{intro}. \end{document} Example of Sections in LaTeX article_sections_ex.tex Example of Sections in LaTeX article_sections_ex.tex \documentclass[12pt]{article} \begin{document} \section{INTRODUCTION} \label{intro} This is section~\ref{intro}. Section~\ref{methods} will follow. \section{NOTATION AND METHODS} \label{methods} This is section~\ref{methods} , which follows section~\ref{intro}. \section{RESULTS} \label{results} This is section 3. \subsection{ARE OF METHOD FOR${\bf log(\hat{RR})}$RELATIVE TO FULL VERIFICATION} \label{arefull} This is subsection~\ref{arefull}, which is within section~\ref{results}. \subsection{ARE OF METHOD FOR${\bf log(\hat{RR})}$RELATIVE TO BG APPROACH} \label{arebg} This is subsection~\ref{arebg}, which is within section~\ref{results}. \section{CONCLUSIONS} \label{last} This is section~\ref{last}. The first section was section~{intro}. \newpage \tableofcontents \end{document} Example 2 of Sections in LaTeX article_sections_ex2.tex Example 2 of Sections in LaTeX article_sections_ex2.tex Example of Journal Responses in LaTeX \documentclass[12pt]{article} \begin{document} \setcounter{page}{1} \centerline{\underline{\bf \large Responses to Referees Comments}} \,\ \vspace{-8pt} \\ The reviewers provided many helpful comments, and the manuscript has benefitted tremendously from the collective guidance. We thank the reviewers. \,\ \vspace{-13pt} \\ \centerline{\underline{\bf Responses to Referee A minor points\'\'}} \,\ \vspace{-13pt} \\ {\it Page 12: Is the bootstrap estimate of the sampling covariance matrix recomputed for each permutation of the data?} \\ Yes, it is recomputed for each permutation. This is stated in Step 4b of elaboration of the coranova procedure on page 12. Additionally, the statement For each random permutation, the bootstrap estimate of$V$,$\widehat{V}_{Boot}$is estimated in the process of estimating$S_B$.\'\' has been added (page 10, 5 lines from bottom). \,\ \vspace{-1pt} \\ \centerline{\underline{\bf Responses to Referee B comments}} \,\ \vspace{-35pt} \\ \begin{enumerate} \item The manuscript does presume some statistical background. ... \item We performed additional comparisons to other approaches, as the reviewer suggested, and found important results. We thank the reviewer for their comment. \end{enumerate} \end{document} responses.tex Example of Letter in LaTeX \documentstyle[12pt]{letter} \raggedbottom \textwidth=6.2in \textheight=8.5in \oddsidemargin=.0in \evensidemargin=.0in \headheight=-.6in \parskip=12pt \parindent=0.25in \address{\,\ \vspace{0.3in} \\ } \signature{Warren Bilker, Ph.D.} \begin{document} \begin{letter}{Roger E. Millsap \\ {\it Editor, MBR} \\ Department of Psychology \\ Arizona State University \\ 950 South McAllister Drive \\ Tempe, AZ 85287-1104 \\ } \opening{\noindent{Professor Millsap:}} We are submitting a revised and final version of the manuscript entitled A Two Factor ANOVA-like Test for Correlated Correlations: CORANOVA\'\', for publication in Multivariate Behavioral Research. ... Please send correspondences to: \\ \,\ \\ Warren Bilker, PhD \\ University of Pennsylvania, School of Medicine \\ Department of Biostatistics and Epidemiology \\ Room 601, Blockley Hall \\ 423 Guardian Drive \\ Phila., PA 19104-6021 Thank you for the opportunity to have our work appear in Multivariate Behavioral Research. \closing{Sincerely,} \cc{ Colleen Brensinger, M.S. \\ Ruben C. Gur, Ph.D. } \end{letter} \end{document} letter_ex1.tex Example of Inserting Picture in LaTeX C:/FILES/PROJECTS/BSTA670/LaTeX_Maple_Mathematica/picture1.jpg \documentclass[12pt]{article} \usepackage{graphicx} \graphicspath{% {converted_graphics/}% inserted by PCTeX {C:/}% inserted by PCTeX } \begin{document} This is an example of inserting a picture in a LaTeX file. \begin{figure}[h] % float placement: (h)ere, page (t)op, page (b)ottom, other (p)age \centering % file name: C:/FILES/PROJECTS/BSTA670/LaTeX_Maple_Mathematica/picture1.jpg \includegraphics[width=5.67in,height=4.25in,keepaspectratio]{picture1} \caption{Nice scenery} \label{picture1} \end{figure} The picture above is figure~\ref{picture1}. \end{document} picture_ex1.tex Example of Slides in LaTeX using Beamer \documentclass[pdf,t]{beamer} \usepackage{graphicx} \usepackage{bm} \setbeamertemplate{footline}[page number] \title{BSTA 670 (Fall 2008) - Statistical Computing \\ \vskip2ex Lecture 9\\ \vskip2ex Optimization II} \author{} \date{} \begin{document} \maketitle \begin{frame} \frametitle{Nelder-Mead Simplex Method} Beamer_ex1.tex (1 of 3) Example of Slides in LaTeX using Beamer \begin{itemize} \item The vector of parameters in K dimensions,$\bm\theta$is to be minimized. A K-dimensional simplex, K-simplex, is defined by K+1 points in K-space (in 1D, a line segment is defined by 2 points). \item Select a starting point for$\bm\theta$,$\bm\theta_0$. \item Compute the centroid (average of the points of the K-simplex OR center of mass of the K-simplex). \tilde{\bm\theta}_{(0)} = \frac{1}{K+1} \sum_{i=0}^{K} \bm\theta_{0i} \quad.\nonumber \item Do a 1-D search over$\bm\theta_K + \alpha

(\tilde{\bm\theta}_{(K)}-\bm\theta_K)$, where$\alpha\in[0,2]$, to find the next$\bm\theta_K$. \item Repeat until convergence. \end{itemize} \end{frame} Beamer_ex1.tex (2 of 3) Example of Slides in LaTeX using Beamer \begin{frame} \frametitle{A Model Problem: Widow\'s Pension Fund} \begin{itemize} \item We will demonstrate several of the optimization methods discussed on the widow\'s pension fund problem that we used earlier for root finding. \item Recall that this problem was to determine the parameters of a mixed model: the mixture parameter$\xi$and the Poisson intensity$\lambda$. \item The log likelihood for this problem was {\footnotesize \begin{eqnarray*} \ell (\xi , \lambda) & = & n_0 \log \left( \xi + (1-\xi) e^{-\lambda} \right) + (N-n_0) \left[\log(1-\xi)-\lambda\right] \\ & + & \sum_{i=1}^{\infty} i \,\ n_i \log\lambda \quad. \end{eqnarray*} } \end{itemize} \end{frame} \end{document} Beamer_ex1.tex (3 of 3) Example 2 of Slides in LaTeX using Beamer Berkeley Theme Slides \documentclass[pdf,t]{beamer} \usetheme{Berkeley} \usepackage{graphicx} \usepackage{bm} \setbeamertemplate{footline}[page number] \title{BSTA 670 (Fall 2008) - Statistical Computing \\ \vskip2ex Lecture 9\\ \vskip2ex Optimization II} \author{} \date{} \begin{document} \maketitle \begin{frame} \frametitle{Nelder-Mead Simplex Method} Beamer_ex1.tex (1 of 3) Other Presentation Themes for Beamer Without Navigation Bars: default, Bergen, Boadilla, Madrid, AnnArbor, CambridgeUS, Pittsburgh, Rochester With a Navigation Bar: Antibes, JuanLesPins, Montpellier With a table of contents: Berkeley, PaloAlto, Goettingen, Marburg, Hannover With Mini Frame Navigation: Berlin, Ilmenau, Dresden, Darmstadt, Frankfurt, Singapore, Szeged With Section and Subsection Table: Copenhagen, Luebeck, Malmoe, Warsaw Beamer_ex2.tex Output Example 3 of Slides in LaTeX using Beamer \documentclass[pdf,t]{beamer} \usepackage{graphicx} \usepackage{bm} \setbeamertemplate{footline}[page number] \setbeamercolor{normal text}{bg=yellow!25} \title{BSTA 670 (Fall 2008) - Statistical Computing\\ \vskip2ex Lecture 9\\ \vskip2ex \textcolor{brown}{Optimization II}} \author{} \date{} \begin{document} \maketitle Beamer_ex3.tex (1 of 3) Example 3 of Slides in LaTeX using Beamer \begin{frame} \frametitle{Nelder-Mead Simplex Method} \begin{itemize} \item The vector of \textcolor{green}{parameters in K dimensions} ,$\bm\theta$is to be minimized. A K-dimensional simplex, K-simplex, is defined byK+1 points in K-space (in 1D, a line segment is defined by 2points). \item Select a starting point for$\bm\theta$,$\bm\theta_0$. \item Compute the centroid (average of the points of the K-simplex ORcenter of mass of the K-simplex). \tilde{\bm\theta}_{(0)} = \frac{1}{K+1} \sum_{i=0}^{K} \bm\theta_{0i} \quad.\nonumber \item Do a 1-D search over$\bm\theta_K + \alpha

(\tilde{\bm\theta}_{(K)}-\bm\theta_K)$, where$\alpha\in[0,2]$, to find the next$\bm\theta_K$. \item \textcolor{blue}{Repeat until convergence}. \end{itemize} \end{frame} Beamer_ex3.tex (2 of 3) Example 3 of Slides in LaTeX using Beamer \begin{frame} \frametitle{A Model Problem: Widow\'s Pension Fund} \begin{itemize} \item We will demonstrate several of the optimization methods discussed on the widow\'s pension fund problem that we used earlier for root finding. \item Recall that this problem was to determine the parameters of a mixed model: the mixture parameter$\xi$and the Poisson intensity$\lambda\$.

\item The log likelihood for this problem was

\textcolor{red}{

{\footnotesize

\begin{eqnarray*}

\ell (\xi , \lambda)

& = & n_0 \log \left( \xi + (1-\xi) e^{-\lambda} \right)

+ (N-n_0) \left[\log(1-\xi)-\lambda\right] \\

& + & \sum_{i=1}^{\infty} i \,\ n_i \log\lambda \quad.

\end{eqnarray*}

}

}

\end{itemize}

\end{frame}

\end{document}

Beamer_ex3.tex (3 of 3)