Histogram vectors

Histograms as 2D or 3D vectors for new physics searches with a background-only and S+B fit to observed data.

A simple histogram with just two bins, comparing a B-only an S+B model to observed data.

The above two-bin histograms can be converted to 2D vectors.

Systematic variations of the S+B histogram.

Systematic variations represented by vector (differences).

A simple histogram with just three bins, comparing a B-only an S+B model to observed data.

The above three-bin histograms represented by 3D vectors. The vectors of the two models and observed data span a unique 2D plane in 3D. This can be easily generalized to

Defining an orthonormal basis in the 2D plane.

Edit and compile if you like:

% Author: Izaak Neutelings (November 2021)
% Inspiration: Kyle Cormier
\documentclass[border=3pt,tikz]{standalone}
\usepackage{physics}
\usepackage{tikz}
\usepackage{tikz-3dplot}
%\usepackage[outline]{contour} % glow around text
\usepackage{xcolor}
\colorlet{myred}{red!70!black}
\colorlet{myblue}{blue!80!black}
\colorlet{mygreen}{green!50!black}
\colorlet{myorange}{orange!80!black}
\colorlet{mydarkred}{red!40!black}
\colorlet{mydarkblue}{blue!40!black}
\colorlet{mydarkgreen}{green!30!black}
\colorlet{mydarkorange}{orange!60!black}
\tikzset{>=latex} % for LaTeX arrow head
\tikzstyle{vector}=[->,mygreen,thick,line cap=round]
\tikzstyle{dot}=[circle,inner sep=0.8,outer sep=0.02]
%\contourlength{1.3pt}
\newcommand*{\vv}[1]{\vec{\mkern0mu#1}} % aligned vector arrow
\def\tick#1{\draw[thick] (#1) --++ (0,0.08);}
\def\point#1#2{
\fill (#1) circle(0.02);
\draw[line width=0.65] (#1)++(0,#2) --++ (0,-2*#2);
\draw[line width=0.65] (#1)++(-0.03,#2) --++ (0.06,0);
\draw[line width=0.65] (#1)++(-0.03,-#2) --++ (0.06,0);
}
\begin{document}
% HISTOGRAM - 2 bins
\begin{tikzpicture}[scale=2.4]
\coordinate (O) at (0,0,0);
\def\w{0.48}
% HISTOGRAMS
\draw[thick,myblue,fill=myblue!6]
(0,0) -- (0,0.79) -| (\w,0.54) -| (2*\w,0) -- cycle;
 
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Click to download: histogram_vectors.texhistogram_vectors.pdf
Open in Overleaf: histogram_vectors.tex

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