small changesHEADmaster

1 files changed, 122 insertions, 66 deletions

diff --git a/pkg/vignettes/IPSUR.Rnw b/pkg/vignettes/IPSUR.Rnw
index 0a40b5a..e9875ba 100644
--- a/pkg/vignettes/IPSUR.Rnw
+++ b/pkg/vignettes/IPSUR.Rnw
@@ -69,8 +69,9 @@
 %\geometry{verbose,tmargin=1in,bmargin=1in,outer=1.25in,inner=0.75in}
 %\geometry{paperwidth=6in,paperheight=9in, margin=0.55in}
 %\geometry{paperwidth=6in,paperheight=9in, margin=0.75in}
-\usepackage[paperwidth=6in,paperheight=9in,tmargin=0.75in,bmargin=0.8in,outer=0.5in,inner=0.75in]{geometry}
+%\usepackage[paperwidth=6in,paperheight=9in,tmargin=0.75in,bmargin=0.8in,outer=0.5in,inner=0.75in]{geometry}
 %\geometry{paperwidth=6in,paperheight=9in,tmargin=0.75in,bmargin=0.8in,outer=0.5in,inner=0.75in}
+\usepackage[paperwidth=7.25in,paperheight=10.25in,tmargin=0.75in,bmargin=0.8in,outer=0.5in,inner=0.75in]{geometry}
 %\geometry{paperwidth=7in,paperheight=10in,tmargin=0.75in,bmargin=0.75in,outer=0.5in,inner=0.75in}
 \pagestyle{headings}
 \setcounter{secnumdepth}{2}
@@ -2418,10 +2419,7 @@ some hidden structure to the data.
 
 \subsubsection{How to do it with \textsf{R}}
 
-The quickest way to visually identify outliers is with a boxplot,
-described above. Another way is with the \texttt{boxplot.stats} function.
-
-
+The quickest way to visually identify outliers is with a boxplot, described above. Another way is with the \texttt{boxplot.stats} function.
 
 \begin{example}[Lengths of Major North American Rivers]
 We will look for potential outliers in the \texttt{rivers} data.
@@ -2552,21 +2550,49 @@ output, of course, but it was Farquar and Farquar in who rightly said
 that ``Getting information from a table is like extracting sunbeams
 from a cucumber.''  We try visual displays to learn about the data.
 
-<<>>=
+<<echo=TRUE, eval=FALSE>>=
+barplot(A, legend.text = TRUE, args.legend = list(x="topleft"))
+barplot(A, legend.text = TRUE, beside = TRUE, args.legend = list(x="topleft"))
+@
+
+
+<<barplots-Titanic, echo=FALSE, fig=TRUE, include=FALSE, height=4,width=6.5>>=
 par(mfrow=c(1,2))
 barplot(A, legend.text = TRUE, args.legend = list(x="topleft"))
 barplot(A, legend.text = TRUE, beside = TRUE, args.legend = list(x="topleft"))
 par(mfrow=c(1,1))
 @
 
+\begin{figure}
+\begin{center}
+\includegraphics{IPSUR-barplots-Titanic}
+\end{center}
+\vspace{-0.5in}
+\caption[Bar plots of the \texttt{Titanic} data.]{{\small Bar plots of the \texttt{Titanic} data.}}
+\label{fig:barplots-Titanic}
+\end{figure}
+
+<<echo=TRUE, eval=FALSE>>=
+spineplot(A)
+mosaicplot(A)
+@
+
 
-<<>>=
+<<spineplot-Titanic, echo=FALSE, fig=TRUE, include=FALSE, height=4,width=6.5>>=
 par(mfrow=c(1,2))
 spineplot(A)
 mosaicplot(A)
 par(mfrow=c(1,1))
 @
 
+\begin{figure}
+\begin{center}
+\includegraphics{IPSUR-spineplot-Titanic}
+\end{center}
+\vspace{-0.5in}
+\caption[Spine and Mosaic plots of the \texttt{Titanic} data.]{{\small Spine and Mosaic plots of the \texttt{Titanic} data.}}
+\label{fig:spineplot-Titanic}
+\end{figure}
 
 
 \subsubsection{Quantitative versus Quantitative}
@@ -2574,7 +2600,7 @@ par(mfrow=c(1,1))
 Two quantitative variables are usually displayed with some sort of scatter plot.
 
 \begin{example}[Reaction Velocity of an Enzymatic Reaction]
-The \texttt{Puromycin} data records the reaction velocity (\texttt{rate}) versus substrate concentration (\texttt{conc}) in an enzymatic reaction involving untreated cells or cells treated with Puromycin.  A scatterplot of the two variables is in Figure BLANK.  We see that rate increases as concentration increases, and in a nonlinear fashion.
+The \texttt{Puromycin} data records the reaction velocity (\texttt{rate}) versus substrate concentration (\texttt{conc}) in an enzymatic reaction involving untreated cells or cells treated with Puromycin.  A scatterplot of the two variables is in Figure~ref{}.  We see that rate increases as concentration increases, and in a nonlinear fashion.
 \end{example}
 
 \begin{example}[The Joyner–Boore Attenuation Data]
@@ -2634,7 +2660,7 @@ par(mfrow=c(1,1))
 
 \subsubsection{Qualitative versus Qualitative}
 
-We will talk about this more in Section \@ref{sec:comparing-data-sets}.
+We will talk about this more in Section~\ref{sec:comparing-data-sets}.
 
 \subsection{Multivariate Data} \label{sub:multivariate-data}
 
@@ -2642,12 +2668,14 @@ Multivariate Data Display
 
 \begin{itemize}
 \item Multi-Way Tables. You can do this with \texttt{table}, or in \textsf{R}
-  Commander by following \texttt{Statistics} \(\triangleright\) \texttt{Contingency
-  Tables} \(\triangleright\) \texttt{Multi-way Tables}.
-\item Scatterplot matrix. used for displaying pairwise scatterplots
-  simultaneously. Again, look for linear association and correlation.
+Commander by following \texttt{Statistics} \(\triangleright\) \texttt{Contingency Tables} \(\triangleright\) \texttt{Multi-way Tables}.
+
+\item Scatterplot matrix. used for displaying pairwise scatterplots simultaneously. Again, look for linear association and correlation.
+
 \item 3D Scatterplot. See Figure~\ref{fig:3D-scatterplot-trees}
+
 \item \texttt{plot(state.region, state.division)}
+
 \item \texttt{barplot(table(state.division,state.region), legend.text=TRUE)}
 \end{itemize}
 
@@ -2665,6 +2693,7 @@ z
 mosaicplot(z, main = "Relation between eye color and sex")
 @
 
+
 \section{Comparing Populations} \label{sec:comparing-data-sets}
 
 Sometimes we have data from two or more groups (or populations) and we
@@ -2944,7 +2973,7 @@ Case in point: in 2015, the Planned Parenthood organization was the
 target of a highly publicized investigation after a series of videos
 were released to the media that allegedly showed Planned Parenthood
 executives discussing potential illicit sale of fetal tissues.  The President of Planned Parenthood, Cecile Richards, testified before a House
-Oversight Committee as part of the investigation. Rep. Jason Chaffetz
+Oversight Committee as part of the investigation. At the time, Rep. Jason Chaffetz
 (R-UT) was the chair of the committee, and near the end of his
 inquiry, he presented the following graph to Richards and asked her
 questions about it. (See Figure~\ref{fig:PPb}.)
@@ -3174,15 +3203,26 @@ and descriptive statistics.
 
 
 
-
-<<echo = FALSE>>=
+<<histexr, echo=FALSE, fig=TRUE, include=FALSE, height=3.5,width=5>>=
 m = sample(25:95, size = 1)
 x = rexp(500, rate = m)
 hist(x, main = "", breaks = 15, xlab="")
 @
 
+\begin{figure}
+\begin{center}
+\includegraphics{IPSUR-histexr}
+\end{center}
+\caption{{\small Some data of interest to a researcher.}}
+\label{fig:histexr}
+\end{figure}
+
+
+<<echo = FALSE>>=
+@
+
 \begin{Exercise}[]
-The data graphed above represent measurements on some quantitative continuous
+The data graphed in Figure~\ref{fig:histexr} represent measurements on some quantitative continuous
 variable of interest to a researcher.
 
 \begin{enumerate}
@@ -9214,18 +9254,24 @@ f_{Y|x}(y|x)=\frac{f_{X,Y}(x,y)}{f_{X}(x)},\quad y\in S_{Y}.
 \end{equation}
 We define \(f_{X|y}\) in a similar fashion.
 
-BLANK
-
-
-
 \begin{example}[]
 Let the joint PMF of \(X\) and \(Y\) be given by
 \[
-f_{X,Y}(x,y) = x + y,\ 0\leq x \leq 1, \ 0 \leq y \leq 1.
+f_{X,Y}(x,y) = x + y,\ 0 \leq x \leq 1, \ 0 \leq y \leq 1.
 \]
 Then the marginal PDF of \(X\) is:
+\[
+f_{X}(x) = \int_{0}^{1} \left(x + y\right)\,\mathrm{d}y =\left. xy + y^{2} \right|_{x=0}^{1} = x + 1,
+\]
+for any \(0 < x < 1\).  Let's fix \(x = 0.5\).  Then the conditional PDF of $Y$ given that $X = 0.5$ will be
+\[
+f_{Y|0.5}(y \vert 0.5) = \frac{f_{X,Y}(0.5, y)}{f_{X}(0.5)} = \frac{0.5 + y}{0.5 + 1} = \frac{2}{3}\left(0.5 + y\right),
+\]
+for all $0< y < 1$.
+
 \end{example}
 
+
 \subsection{Bayesian Connection}
 
 Conditional distributions play a fundamental role in Bayesian
@@ -9886,15 +9932,9 @@ Theorem~\ref{thm:mvnorm-dist-matrix-prod}.
 
 \subsubsection{How to do it with \textsf{R}} \label{sub:bivariate-transf-r}
 
-It is possible to do the computations above in \textsf{R} with the
-\texttt{Ryacas} package. The package is an interface to the open-source
-computer algebra system, ``Yacas''. The user installs Yacas, then
-employs \texttt{Ryacas} to submit commands to Yacas, after which the output
-is displayed in the \textsf{R} console.
+It is possible to do the computations above in \textsf{R} with the \texttt{Ryacas} package. The package is an interface to the open-source computer algebra system, ``Yacas''. The user installs Yacas, then employs \texttt{Ryacas} to submit commands to Yacas, after which the output is displayed in the \textsf{R} console.
 
-There are not yet any examples of Yacas in this book, but there are
-online materials to help the interested reader: see
-\url{http://code.google.com/p/ryacas/} to get
+There are not yet any examples of Yacas in this book, but there are online materials to help the interested reader: see \url{http://r-cas.github.io/ryacas/} to get
 started.
 
 \section{Remarks for the Multivariate Case} \label{sec:remarks-for-the-multivariate}
@@ -10478,7 +10518,7 @@ consult Casella and Berger \cite{Casella2002}, or Hogg \textit{et al}
 \end{proof}
 
 
-\subsection{The Distribution of Student's \(t\) Statistic} \label{sub:students-t-distribution}
+\subsection{The Distribution of Student's \(t\) Statistic} \label{sub:student-t-distribution}
 
 
 \begin{prop}[]
@@ -11213,6 +11253,7 @@ curve(x^3*(1-x)^4, 0, 1, add = TRUE)
 \begin{center}
 \includegraphics{IPSUR-fishing-part-two}
 \end{center}
+\vspace{-0.35in}
 \caption[Assorted likelihood functions for fishing, part two.]{{\small Assorted likelihood functions for fishing, part two.   Three graphs are shown of \(L\) when \(\sum x_{i}\) equals 3, 4, and 5, respectively, from left to right. We pick an \(L\) that matches the observed data and then maximize \(L\) as a function of \(p\). If \(\sum x_{i}=4\), then the maximum appears to occur somewhere around \(p \approx 0.6\).}}
 \label{fig:fishing-part-two}
 \end{figure}
@@ -11272,6 +11313,7 @@ text(mle, mleobj/4, substitute(hat(theta)==a, list(a=round(mle, 4))), cex = 1.3,
 \begin{center}
 \includegraphics{IPSUR-species-mle}
 \end{center}
+\vspace{-0.35in}
 \caption[Species maximum likelihood.]{{\small Species maximum
     likelihood.  Here we see that
     \(\hat{\theta} \approx \Sexpr{round(mean(dat),2)}\) is the
@@ -11385,9 +11427,9 @@ where \(\hat{\mu}=\overline{X}\) and
 We of course know from \@ref{pro:mean-sd-xbar} that \(\hat{\mu}\) is
 unbiased. What about \(\hat{\sigma^{2}}\)? Let us check:
 \begin{eqnarray*}
-\mathbb{E}\,\hat{\sigma^{2}} & = & \mathbb{E}\,\frac{n-1}{n}S^{2}\\
- & = & \mathbb{E}\left(\frac{\sigma^{2}}{n}\frac{(n-1)S^{2}}{\sigma^{2}}\right)\\
- & = & \frac{\sigma^{2}}{n}\mathbb{E}\ \mathsf{chisq}(\mathtt{df}=n-1)\\
+\mathbb{E}\,\hat{\sigma^{2}} & = & \mathbb{E}\,\frac{n-1}{n}S^{2},\\
+ & = & \mathbb{E}\left(\frac{\sigma^{2}}{n}\frac{(n-1)S^{2}}{\sigma^{2}}\right),\\
+ & = & \frac{\sigma^{2}}{n}\mathbb{E}\ \mathsf{chisq}(\mathtt{df}=n-1),\\
  & = & \frac{\sigma^{2}}{n}(n-1),
 \end{eqnarray*}
 from which we may conclude two things:
@@ -19866,7 +19908,8 @@ also has a \texttt{write.matrix} function.
 \texttt{stack}
 
 
-\chapter{Mathematical Machinery} \label{cha:mathematical-machinery}
+\chapter{Mathematical Machinery} 
+\label{cha:mathematical-machinery}
 
 This appendix houses many of the standard definitions and theorems
 that are used at some point during the narrative. It is targeted for
@@ -19880,8 +19923,8 @@ Folland \cite{Folland1999}, or Carothers \cite{Carothers2000}), or
 Measure Theory (Billingsley \cite{Billingsley1995}, Ash
 \cite{Ash2000}, Resnick \cite{Resnick1999}) for details.
 
-\section{Set Algebra} \label{sec:the-algebra-of}
-
+\section{Set Algebra} 
+\label{sec:the-algebra-of}
 
 We denote sets by capital letters, \(A\), \(B\), \(C\), \textit{etc}. The
 letter \(S\) is reserved for the sample space, also known as the
@@ -19911,7 +19954,6 @@ Complement    & $A^{c}$               & in $S$ but not in $A$ & \texttt{setdiff(
 \label{tab:set-operations}
 \end{table}
 
-
 \subsection{Identities and Properties}
 
 \begin{enumerate}
@@ -19994,12 +20036,20 @@ if \(f'(a)\) exists. It is \textit{differentiable on an open interval}
 In the table that follows, \(f\) and \(g\) are differentiable
 functions and \(c\) is a constant.
 
-(ref:tab-differentiation-rules)
-
-Table: Differentiation rules.
-
-| \(\frac{\mathrm{d}}{\mathrm{d} x}c=0\) | \(\frac{\mathrm{d}}{\mathrm{d} x}x^{n}=nx^{n-1}\) | \((cf)'=cf'\)                                       |
-| \((f\pm g)'=f'\pm g'\)       | \((fg)'=f'g+fg'\)                       | \(\left(\frac{f}{g}\right)'=\frac{f'g-fg'}{g^{2}}\) |
+\begin{table}[H]
+\begin{centering}
+\begin{tabular}{|c|c|c|}
+\hline 
+ &  & \tabularnewline
+$\frac{\mathrm{d}}{\mathrm{d} x}c=0$ & $\frac{\mathrm{d}}{\mathrm{d} x}x^{n}=nx^{n-1}$ & $(cf)'=cf'$\tabularnewline
+ &  & \tabularnewline
+$(f\pm g)'=f'\pm g'$ & $(fg)'=f'g+fg'$ & $\left(\frac{f}{g}\right)'=\frac{f'g-fg'}{g^{2}}$\tabularnewline
+ &  & \tabularnewline
+\hline
+\end{tabular}
+\par\end{centering}
+\caption{Differentiation rules\textbf{\label{tab:differentiation-rules}}}
+\end{table}
 
 
 
@@ -20011,13 +20061,20 @@ differentiable and \(F'(x) = f'[ g(x) ] \cdot g'(x)\).
 
 \subsubsection{Useful Derivatives}
 
-(ref:tab-useful-derivatives)
-
-Table: Some derivatives.
-
-| \(\frac{\mathrm{d}}{\mathrm{d} x}\mathrm{e}^{x}=\mathrm{e}^{x}\) | \(\frac{\mathrm{d}}{\mathrm{d} x}\ln x=x^{-1}\)     | \(\frac{\mathrm{d}}{\mathrm{d} x}\sin x=\cos x\)             |
-| \(\frac{\mathrm{d}}{\mathrm{d} x}\cos x=-\sin x\)  | \(\frac{\mathrm{d}}{\mathrm{d} x}\tan x=\sec^{2}x\) | \(\frac{\mathrm{d}}{\mathrm{d} x}\tan^{-1}x=(1+x^{2})^{-1}\) |
-|                                        |                                         |                                                  |
+\begin{table}[H]
+\begin{centering}
+\begin{tabular}{|c|c|c|}
+\hline 
+ &  & \tabularnewline
+$\frac{\mathrm{d}}{\mathrm{d} x}\mathrm{e}^{x}=\mathrm{e}^{x}$ & $\frac{\mathrm{d}}{\mathrm{d} x}\ln x=x^{-1}$ & $\frac{\mathrm{d}}{\mathrm{d} x}\sin x=\cos x$\tabularnewline
+ &  & \tabularnewline
+$\frac{\mathrm{d}}{\mathrm{d} x}\cos x=-\sin x$ & $\frac{\mathrm{d}}{\mathrm{d} x}\tan x=\sec^{2}x$ & $\frac{\mathrm{d}}{\mathrm{d} x}\tan^{-1}x=(1+x^{2})^{-1}$$ $\tabularnewline
+ &  & \tabularnewline
+\hline
+\end{tabular}
+\par\end{centering}
+\caption{Some derivatives\textbf{\label{tab:useful-derivatives}}}
+\end{table}
 
 \subsection{Optimization}
 
@@ -20027,7 +20084,6 @@ which \(f'(x^{\ast})=0\) or for which \(f'(x^{\ast})\) does not exist.
 \end{defn}
 
 
-
 \begin{thm}[First Derivative Test]
 \label{thm:first-derivative-test}
 If \(f\) is differentiable and if
@@ -20101,22 +20157,26 @@ If \(g\) is a differentiable function whose range is the interval
 
 \subsubsection{Useful Integrals}
 
-(ref:tab-useful-integrals)
-
-Table: Some integrals (constants of integration omitted).
-
-| \(\int x^{n}\,\mathrm{d} x=x^{n+1}/(n+1),\ n \neq - 1\) | \(\int\mathrm{e}^{x}\,\mathrm{d} x=\mathrm{e}^{x}\) | \(\int x^{-1}\,\mathrm{d} x=\ln \mathrm{abs}(x) \) |
-| \(\int\tan x\:\mathrm{d} x=\ln \mathrm{abs}(\sec x)\) | \(\int a^{x}\,\mathrm{d} x=a^{x}/\ln a\)            | \(\int(x^{2}+1)^{-1}\,\mathrm{d} x=\tan^{-1}x\) |
-
+\begin{table}[H]
+\begin{centering}
+\begin{tabular}{|c|c|c|}
+\hline 
+ &  & \tabularnewline
+$\int x^{n}\,\mathrm{d} x=x^{n+1}/(n+1),\ n\neq-1$ & $\int\mathrm{e}^{x}\,\mathrm{d} x=\mathrm{e}^{x}$ & $\int x^{-1}\,\mathrm{d} x=\ln|x|$\tabularnewline
+ &  & \tabularnewline
+$\int\tan x\:\mathrm{d} x=\ln|\sec x|$ & $\int a^{x}\,\mathrm{d} x=a^{x}/\ln a$ & $\int(x^{2}+1)^{-1}\,\mathrm{d} x=\tan^{-1}x$\tabularnewline
+ &  & \tabularnewline
+\hline
+\end{tabular}
+\par\end{centering}
+\caption{Some integrals (constants of integration omitted)\textbf{\label{tab:useful-integrals}}}
+\end{table}
 \subsubsection{Integration by Parts}
 
 \begin{equation}
 \int u\:\mathrm{d} v=uv-\int v\:\mathrm{d} u
 \end{equation}
 
-
-
-
 \begin{thm}[L'H\^ opital's Rule]
 Suppose \(f\) and \(g\) are differentiable and \(g'(x)\neq0\) near
 \(a\), except possibly at \(a\). Suppose that the limit
@@ -20390,8 +20450,6 @@ compute the determinant; the final result is independent of the \(j\)
 chosen.
 \end{defn}
 
-
-
 \begin{fact}[]
 The determinant of the \(2\times2\) matrix
 \begin{equation}
@@ -20400,8 +20458,6 @@ c & d\end{bmatrix}\quad \mbox{is} \quad |\mathbf{A}|=ad-bc.
 \end{equation}
 \end{fact}
 
-
-
 \begin{fact}[]
 A square matrix \(\mathbf{A}\) is nonsingular if and only if
 \(\mathrm{det}(\mathbf{A})\neq0\).