# LaTeX Tips

July 28, 2008

## Contents

- Add backlinks to the bibliography
- Stochastic independence
- Roots
- Natbib
- Conditional Probability and Expectation

## Add Backlinks to the Bibliography

You can add backlinks to the end of bibliography items using the
`hyperref`

package as follows:

```
\usepackage[backref]{hyperref}
```

This will add links to the *section* where each reference was cited.
If you prefer to link to the *page*, use

```
\usepackage[pagebackref]{hyperref}
```

instead. The style of the links can be customized by modifying the
`\backref`

and `\backrefalt`

macros as described in the `hyperref`

README file. For example, to place the backlinks in square brackets,
use:

```
\renewcommand*{\backref}[1]{[#1]}
```

The result is a bibliography entry like the following:

Künsch, H. R. (2005). Recursive Monte Carlo filters: algorithms and theoretical analysis.

Annals of Statistics33, 1983–2021. [3, 27]

where 3 and 27 are hyperlinks to the pages where the paper was cited.

## Stochastic Independence

The stochastic independence symbol is not part of LaTeX itself, nor is it
included in any of the AMS-LaTeX packages. The closest thing is `\perp`

or `\bot`

. There is, however, a `\Perp`

macro defined in the
`txfonts`

/`psfonts`

packages but these change the default fonts. Here
is a cheap hack that fakes the symbol by using two `\perp`

s separarated
by some negative spacing:

```
\newcommand{\Perp}{\perp \! \! \! \perp}
```

The macro above is not robust to different math fonts, however,
Donald Arseneau posted the following definition of an independence symbol
to `comp.text.tex`

which works well with any font:

```
\newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}}
\def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}
```

## Roots

`\sqrt{n}`

will produce the square root of `n`

while
`\sqrt[k]{n}`

will produce the `k`

-th root of `n`

.
For example, for the cube root of `n`

use `\sqrt[3]{n}`

.

## Natbib

The Natbib package provides much better default citation behavior as well as finer control over citations in your documents.

```
\usepackage[longnamesfirst]{natbib}
```

The `longnamesfirst`

option prints out all authors in full the first
time a reference is cited and abbreviates subsequent citations using
“et al.” if there are more than two authors.

Natbib provides many new citation commands for citing references in various situations. See the Natbib notes for details.

Natbib also provides several nice bibliography styles such as `chicago`

:

```
\bibliographystyle{chicago}
```

## Conditional Probability and Expectation

For simple, normal sized conditional probability and conditional
expectation expressions, the `\mid`

command from AMS-LaTeX
should be used instead of the pipe (`|`

) or the `\vert`

macro
because it is defined as a binary relation and gets the spacing
right. For example, instead of

```
\Pr( A | B )
```

it is better to write

```
\Pr( A \mid B )
```

However, like braces, parentheses, and other delimiters, `\mid`

is not
stretchy on its own. For taller expressions, such as fractions, there
are two options. LaTeX will try to automatically choose the correct
size if you use a `\left`

, `\middle`

, and `\right`

construct such as
the following:

```
\Pr\left( A \;\middle\vert\; B \right)
```

Note that since `\mid`

is not a stretchy delimiter, we have to use
`\vert`

here and add the spacing manually with the surrounding `\;`

commands.

Alternatively, if you need to control the size manually, the
`\big`

, `\Big`

, `\bigg`

, and `\Bigg`

contructs will be useful:

```
\Pr\bigl( A \bigm\vert B \bigr)
\Pr\Bigl( A \Bigm\vert B \Bigr)
\Pr\biggl( A \biggm\vert B \biggr)
\Pr\Biggl( A \Biggm\vert B \Biggr)
```