Mathematical notation for probability theory
From sets to sparsity and product spaces to priors.
Cheatsheet
Reporting
General
Since my school days, I have lacked confidence in writing mathematical notation. This cheatsheet is here to remedy that!
The notations I list here is all but set in stone, but seems to be least one of the common ways to approach notation in this subject area. It is adapted from Michael Betancourt’s blog
Set notation
| Notation | Interpretation |
|---|---|
| \(X\) | The ambient set captures all objects of interest. |
| \(x\) | A variable element in the ambient set \(X\). |
| \(x_n \in X\) | A specific element \(x_n\) from the ambient set \(X\). |
| \(\text{x}\) | A variable subset of the ambient set \(X\). |
| \(X = \{\text{🥦, 🥫, 🥐}\}\) | A set with a finite number of elements. |
| \(\text{x} \subset X\) | A subset of \(X\). |
| \(\text{x} \subseteq X\) | A subset potentially containing all elements of \(X\). |
| \(\text{x}'\) | A subset of another subset \(\text{x}\). |
| \(\emptyset = \{\}\) | The empty set which contains no elements at all. |
| \(\{x_n\}\) | A subset with a single element is the atomic set1. |
| \(2^X\) | The power set of \(X\) is the collection of all its subsets. |
| \(\text{x} = \{\text{🥦}\}, \text{x}^c = \{\text{🥫, 🥐}\}\) | The complement \(\text{x}^c\) of \(\text{x}\) includes all \(x_n \in X\) not already in \(\text{x}\). |
| \(\{\text{🥦, 🥫}\} \cup \{\text{🥫, 🥐}\} = \{\text{🥦, 🥫, 🥐}\}\) | A union includes all elements found in either subset. |
| \(\{\text{🥦, 🥫}\} \cap \{\text{🥫, 🥐}\} = \{\text{🥫}\}\) | An intersection includes all elements found in both subsets. |
Work in progress
This document will be extended with more chapters!
Footnotes
Atomic vectors finally make sense (looking at you here,
R!).↩︎