> [!note] Notation
> Lowercase letters $f,p,q,$ etc. are pdfs or pmfs.
>
> Uppercase letters $F,P,Q$, etc. are cdfs. $\Phi$ is the standard normal cdf.
>
> Bold letters $\mathbf{X}$ are vector/multi-dimensional random variables.
>
> Variables with hats, e.g. $\hat{\theta}$, are estimates for those without, e.g. $\theta$.
>
> $X \sim p$ is the variable we want to simulate.
>
> $Y \sim q$ are proposal distributions when relevant. The proposal is sometimes written as $X \overset{?}{=}y$.
>
> $U$ are uniform variables, most likely $U[0,1]$.
>
> Subscripts in expectations like $\mathbb{E}_{X}$ specifies the expectation to be integrated over the density of $X \sim p$, as opposed to say $\mathbb{E}_{Y}$ with $Y \sim q$: $\begin{align*}
\mathbb{E}_{X}[\phi(X)]&= \int p(x)\phi(x) \, dx,\\
\mathbb{E}_{Y}[\phi(Y)]&= \int q(y)\phi(y) \, dy,
\end{align*}$which are in general different quantities.
> [!citenotitle]
>
> ```dataview
> table without id
> File as "Topics",
> choice(oneliner, oneliner, "") as "",
> dateformat(file.mtime, "yyyy-MM-dd") as "Last Modified"
> from ""
> FLATTEN "[[" + file.path + "|" + truncate(file.name, 30) + "]]" as File
> where
> (
> (domain and contains(domain, this.file.link)
> and (file.name != this.file.name))
> or
> any(map(file.tags,
> (x) => econtains(this.domain_tags, substring(x, 1))))
> or
> any(map(file.tags,
> (x) => any(map(this.domain_tags,
> (domtag) => contains(x, domtag + "/")))
> ))
> )
> and
> !contains(file.path, "2 - Snippets")
> and
> !contains(file.tags, "subdomain")
> sort file.mtime desc
> ```
>
> [!citenotitle]
>
> ```dataview
> table without id
> File as "Snippets",
> choice(oneliner, oneliner, "") as "",
> dateformat(file.mtime, "yyyy-MM-dd") as "Last Modified"
> from "2 - Snippets"
> FLATTEN "[[" + file.path + "|" + truncate(file.name, 30) + "]]" as File
> where
> (
> (domain and contains(domain, this.file.link)
> and (file.name != this.file.name))
> or
> any(map(file.tags,
> (x) => econtains(this.domain_tags, substring(x, 1))))
> or
> any(map(file.tags,
> (x) => any(map(this.domain_tags,
> (domtag) => contains(x, domtag + "/")))
> ))
> )
> sort file.mtime desc
> ```