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Updates: #34

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16 changes: 8 additions & 8 deletions manuscript/02_probability.md
Original file line number Diff line number Diff line change
Expand Up @@ -109,20 +109,20 @@ Answer: No, the events can simultaneously occur and so
exclusive. To elaborate let:

{$$}
\begin{eqnarray*}
A_1 & = & \{\mbox{Person has sleep apnea}\} \\
A_2 & = & \{\mbox{Person has RLS}\}
\end{eqnarray*}
\begin{aligned}
A_1 & = \{\mbox{Person has sleep apnea}\} \\
A_2 & = \{\mbox{Person has RLS}\}
\end{aligned}
{/$$}

Then

{$$}
\begin{eqnarray*}
P(A_1 \cup A_2 ) & = & P(A_1) + P(A_2) - P(A_1 \cap
\begin{aligned}
P(A_1 \cup A_2 ) & = P(A_1) + P(A_2) - P(A_1 \cap
A_2) \\
& = & 0.13 - \mbox{Probability of having both}
\end{eqnarray*}
& = 0.13 - \mbox{Probability of having both}
\end{aligned}
{/$$}

Given the scenario, it's likely that some fraction of the population has both.
Expand Down
12 changes: 6 additions & 6 deletions manuscript/03_conditional.md
Original file line number Diff line number Diff line change
Expand Up @@ -132,12 +132,12 @@ the specificity, {$$}P(- ~|~ D^c) =.985{/$$} and the prevalence
{$$}P(D) = .001{/$$}.

{$$}
\begin{eqnarray*}
P(D ~|~ +) & = &\frac{P(+~|~D)P(D)}{P(+~|~D)P(D) + P(+~|~D^c)P(D^c)}\\
& = & \frac{P(+~|~D)P(D)}{P(+~|~D)P(D) + \{1-P(-~|~D^c)\}\{1 - P(D)\}} \\
& = & \frac{.997\times .001}{.997 \times .001 + .015 \times .999}\\
& = & .062
\end{eqnarray*}
\begin{aligned}
P(D ~|~ +) & = \frac{P(+~|~D)P(D)}{P(+~|~D)P(D) + P(+~|~D^c)P(D^c)}\\
& = \frac{P(+~|~D)P(D)}{P(+~|~D)P(D) + \{1-P(-~|~D^c)\}\{1 - P(D)\}} \\
& = \frac{.997\times .001}{.997 \times .001 + .015 \times .999}\\
& = .062
\end{aligned}
{/$$}

In this population a positive test result only suggests a 6% probability that
Expand Down
110 changes: 57 additions & 53 deletions manuscript/LittleInferenceBook.Rmd
Original file line number Diff line number Diff line change
@@ -1,53 +1,57 @@
---
output:
html_document:
toc: true
toc_depth: 2
includes:
before_body: frontmatter.html
---


```{r book, results='asis', echo = FALSE}

# Get list of .md files from the LeanPub configuration file
chapters <- readLines(con = "Book.txt")

# Set the encoding
encoding <- "Latin1"

# Output the content of every file
invisible(
sapply(X = chapters, encoding = encoding,
FUN = function(file, encoding){
# Read in file contents
contents <- readLines(con = file, encoding = encoding)

# Replace with correct equation markers
contents <- gsub(pattern = "([{][$]{2}[}] *)|( *[{]/[$]{2}[}])",
replacement = "$$",
x = contents)

# Fix code blocks
contents <- paste(contents, collapse = "\n")
contents <- gsub(pattern = " ~ ", replacement = " \tilde ", x = contents)
contents <- gsub(pattern = paste0("\n[{](title ?= ?\"([^\"]*)\")?",
"[^~]*~~*[[:space:]]*",
"([^~]*)",
"~~*\n"),
replacement = "\n**\\2**\n\n```\n\\3\n```\n\n",
x = contents)
contents <- gsub(pattern = " \\tilde ", replacement = " ~ ", x = contents)

# Identify inline equations
contents <- gsub(pattern = "[$]{2}", replacement = "$", x = contents)
contents <- gsub(pattern = "(\n{2,})[$]([^$]*)[$]",
replacement = "\\1$$\\2$$",
x = contents)

# Output file contents
cat(contents, "\n\n", sep = "")
})
)
```

---
output:
pdf_document:
toc: true
includes:
in_header: title.tex
html_document:
toc: true
toc_depth: 2
includes:
before_body: frontmatter.html
---


```{r book, results='asis', echo = FALSE}

# Get list of .md files from the LeanPub configuration file
chapters <- readLines(con = "Book.txt")

# Set the encoding
encoding <- "Latin1"

# Output the content of every file
invisible(
sapply(X = chapters, encoding = encoding,
FUN = function(file, encoding){
# Read in file contents
contents <- readLines(con = file, encoding = encoding)

# Replace with correct equation markers
contents <- gsub(pattern = "([{][$]{2}[}] *)|( *[{]/[$]{2}[}])",
replacement = "$$",
x = contents)

# Fix code blocks
contents <- paste(contents, collapse = "\n")
contents <- gsub(pattern = " ~ ", replacement = " \tilde ", x = contents)
contents <- gsub(pattern = paste0("\n[{](title ?= ?\"([^\"]*)\")?",
"[^~]*~~*[[:space:]]*",
"([^~]*)",
"~~*\n"),
replacement = "\n**\\2**\n\n```\n\\3\n```\n\n",
x = contents)
contents <- gsub(pattern = " \\tilde ", replacement = " ~ ", x = contents)

# Identify inline equations
contents <- gsub(pattern = "[$]{2}", replacement = "$", x = contents)
contents <- gsub(pattern = "(\n{2,})[$]([^$]*)[$]",
replacement = "\\1$$\\2$$",
x = contents)

# Output file contents
cat(contents, "\n\n", sep = "")
})
)
```

8 changes: 8 additions & 0 deletions manuscript/title.tex
Original file line number Diff line number Diff line change
@@ -0,0 +1,8 @@
\usepackage{titling}
\setlength{\droptitle}{-1in}
\pretitle{%
\begin{center}
\LARGE
\includegraphics{images/title_page.png}\\[\bigskipamount]
}
\posttitle{\end{center}}