How to neatly space the equals sign when using probabilities?

Question

When the equals sign is used as part of the probability notation it looks a little odd when typeset in LaTeX, especially when a lot of equals sign occurs in the same line.

E.g.,

\[ \Pr(A=a) = \Pr(B=b \mid C=c) \]

The spacing between the equal sign is the same for both the 'equal to' relation and the ones between the random variable (A, B, C) and the constants (a, b, c).

Is ther a way to make the spacing between the latter smaller be than the former, or am I just overthinking this?

Answer 1

It's straightforward to define a macro such as \newcommand\myeq{\mkern1.5mu{=}\mkern1.5mu} -- choose the argument of \mkern to suit your personal preferences -- and thus to rewrite your equation as

 \Pr(A\myeq a)  &= \Pr(B\myeq b \mid C\myeq c)

In the TeXbook (p. 174, near bottom of page), though, DEK suggests not reducing the whitespace around the = symbols but, instead, adding more whitespace elsewhere in the full equation via judiciously-placed \, directives:

 \[ \Pr(\, A=a \,) = \Pr(\, B=b \mid C=c \,) \]

A full MWE:

\documentclass{article}
\newcommand\myeq{\mkern1.5mu{=}\mkern1.5mu}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\Pr(A=a)       &= \Pr(B=b \mid C=c) \\           % original form
\Pr(A\myeq a)  &= \Pr(B\myeq b \mid C\myeq c) \\ % less whitespace around "="
\Pr(\, A=a \,) &= \Pr(\, B=b \mid C=c \,)        % *more* whitespace
\end{align*}
\end{document}

Answer 2

I turn my comment to an answer since I think it is an adequate solution, in particular in this situation, and it is simpler than the other approaches. I also find no flaw in its visual appearance. It also makes sense to me logically, since A=a can be viewed as a compound label for an event, not necessarily as an equation. Even if it's an equation, it's just too tiny to be granted the same rights as other equations.

\documentclass{article}
\begin{document}
\[ \Pr(A{=}a) = \Pr(B{=}b \mid C{=}c) \]
\end{document}

Answer 3

This reduces by half the space around the equals sign in the argument to \Pr; it also has the advantage of being able to set the size of the delimiters in an optional argument.

\documentclass{article}
\usepackage{mathtools}

\DeclarePairedDelimiterX\PrArg[1]{(}{)}{%
  \renewcommand\given{\Conditional{\delimsize}}%
  \begingroup\lccode`~=`= \lowercase{\endgroup\let~}\reducedequals
  \edef\equals{\mathchar\the\mathcode`= }%
  \mathcode`="8000
  #1%
}
\providecommand\given{}
\newcommand{\Conditional}[1]{%
  \nonscript\;#1\vert\nonscript\;\mathopen{}%
}
\renewcommand{\Pr}{\operatorname{Pr}\PrArg}
\newcommand{\reducedequals}{%
  \mskip-.5\thickmuskip
  \equals
  \mskip-.5\thickmuskip
  \nobreak
}

\begin{document}

$\Pr{A=a} = \Pr{B=b \given C=c}$

$\Pr[\big]{A=\frac{1}{2}} = \Pr[\Big]{B=b \given C=\sqrt{\frac{a^{2^n}}{b}}}$

\end{document}

Answer 4

This is not for the manual of best practices, but between treat the equal sing as a very spaced math relation (that is the default equivalent to \mathrel{=}) or suppress all this extra space treating the symbol like text (\mbox{=} or \text{=} with amsmat) or simply grouping it ({=}) as gernot pointed, that may be is too drastic, in this case you can simply treat it as an unary or binary operator (\mathop{=} or \mathbin{=} respectively) although syntactically sound odd. To further but not complete shrinkage, another simple option is add negative spaces in both sides (\!=\!). Anyway, it could also a good idea increase a bit the space for the "main equal" sign (with \,=\, for instance). My preference is use both \!=\! and \,=\,. Example:

\documentclass[twocolumn]{article}

%just for the mwe format, no need of preamble code for solutions.
\usepackage{tabto} 
\setlength{\parskip}{.3ex}
\TabPositions{.7\linewidth}

\begin{document}

\( \Pr(A=a) = \Pr(B=b \mid C=c) \) \tab  default\par 
\( \Pr(A\mathrel=a)  = \Pr(B\mathrel=b  \mid C\mathrel=c) \)    \tab  \verb|\mathrel|\par 
\( \Pr(A\mathbin=a)  = \Pr(B\mathbin=b  \mid C\mathbin=c) \)    \tab  \verb|\mathbin|\par
\( \Pr(A\mathop{=}a) = \Pr(B\mathop{=}b \mid C\mathop{=}c) \)   \tab  \verb|\mathop|\par
\( \Pr(A\!=\!a) = \Pr(B\!=\!b \mid C\!=\!c) \)                  \tab  \verb|\!=\!|\par
\( \Pr(A{=}a) = \Pr(B{=}b \mid C{=}c) \)                        \tab  \verb|{=}|\par
$\vdots$\par
\( \Pr(A\!=\!a) \,=\, \Pr(B\!=\!b \mid C\!=\!c) \)      \tab  and  \verb|\,=\,|

\end{document}

Answer 5

\let\originalPr\Pr
\def\Pr(#1){\originalPr(\mathmakebox{\thickmuskip=.5\thickmuskip #1})}

Tweak that .5 at will.

Answer 6

You can re-define the = as binary operator in Pr argument and I recommend to enlarge the \thickmuskip for relations (spacing for the outer = etc.), when such "Pr" equations are commonly used in your document.

\def\Pr(#1){\mathop{\rm Pr}({\mathcode`=="203D #1})}
\multiply\thickmuskip by3 \divide\thickmuskip by2

$ \Pr(A=a) = \Pr(B=b \mid C=c) $

\bye

Answer 7

To get the effect of automatically adding {} around every = inside \Pr, use \scriptstyle to eliminate the space around = and the relsize package to scale back up.

\documentclass{article}
\usepackage{relsize, mathtools}
\renewcommand\Pr[1]{\text{P({\larger[2]$\scriptstyle#1$})}}

\begin{document}
\[\text P(A{=}a) = \text P(B{=}b {\mid} C{=}c)\]
\[\Pr{A=a} = \Pr{B=b \mid C=c}\]
\end{document}

This method will remove space around = as well as <, ≤, +, etc inside \Pr. One operator from which you might not want space removed is the conditional probability pipe \mid.

To remove space from all operators except \mid:

\documentclass{article}
\usepackage{relsize, mathtools}
\renewcommand\Pr[1]{\begingroup
    \renewcommand\mid{\;|\;}
    \text{P({\larger[2]$\scriptstyle#1$})}
    \endgroup}

\begin{document}
\[\Pr{A=a} = \Pr{B=b \mid C=c}\]
\[\scriptstyle \Pr{A=a} = \Pr{B=b \mid C=c}\]
\end{document}

As depicted, this forces space around \mid even in \scriptstyle environments, where operators typically do not have space.

To remove space from \mid in \scriptstyle or \scriptscriptstyle \Pr only:

\documentclass{article}
\usepackage{relsize, mathtools}
\renewcommand\Pr[1]{\begingroup
    \renewcommand\mid{\mathchoice{\;|\;}{\;|\;}{\;|\;}{|}}
    \mathchoice
        {\text{P({\larger[2]$\scriptstyle#1$})}}
        {\text{P({\larger[2]$\scriptstyle#1$})}}
        {\text{P({\larger[4]$\scriptscriptstyle#1$})}}
        {\text{P({\larger[2]$\scriptscriptstyle#1$})}}
    \endgroup}

\begin{document}
\[\Pr{A=a} = \Pr{B=b \mid C=c}\]
\[\scriptstyle \Pr{A=a} = \Pr{B=b \mid C=c}\]
\end{document}