_macros.qmd

<!-- First, some macros specific to this document -->

\newcommand\parm{{(m)}}
\newcommand\expl[1]{\;\;\text{(#1)}}
\newcommand{\red}[1]{{\color{red} #1}}
\newcommand{\sd}{\operatorname{SD}}
\newcommand{\mse}{\operatorname{MSE}}
\newcommand{\rmse}{\operatorname{RMSE}}
\newcommand{\bias}{\operatorname{Bias}}

\newcommand{\ESS}{\operatorname{ESS}}

<!-- -->

<!-- 
Second, tiny-shortex for Quarto
restricted to macros supported by MathJax
https://github.com/trevorcampbell/shortex
-->

<!-- common sets and set operations -->
\newcommand{\reals}{\mathbb{R}}
\newcommand{\ints}{\mathbb{Z}}
\newcommand{\rats}{\mathbb{Q}}
\newcommand{\nats}{\mathbb{N}}
\newcommand{\comps}{\mathbb{C}}

<!-- text shortcuts -->
\newcommand{\iid}{\textrm{i.i.d.}\@\xspace}
\newcommand{\as}{\textrm{a.s.}\@\xspace}
\newcommand{\aev}{\textrm{a.e.}\@\xspace}

<!-- convergence -->
\newcommand{\convas}{\overset{a.s.}{\to}}
\newcommand{\convp}{\overset{p}{\to}}
\newcommand{\convd}{\overset{d}{\to}}
\newcommand{\eqd}{\overset{d}{=}}
\newcommand{\eqas}{\overset{a.s.}{=}}

<!-- unary functions -->
\newcommand{\pr}{\mathbb{P}}  
\newcommand{\ex}{\mathbb{E}}
<!-- \newcommand{\Pr}{\mathbb{P}}   LaTeX Error: Command \Pr already defined. -->
\newcommand{\E}{\mathbb{E}}
\newcommand{\law}{\mathcal{L}} 
\newcommand{\var}{\operatorname{Var}}
\newcommand{\cov}{\operatorname{Cov}}	
\newcommand{\cor}{\operatorname{Corr}}
\newcommand{\supp}{\operatorname{supp}} 

<!-- Min and max -->
\def\argmax{\operatorname{arg\,max}}
\def\argmin{\operatorname{arg\,min}}
\def\esssup{\operatorname{ess\,sup}}
\def\essinf{\operatorname{ess\,inf}}


<!-- binary operators -->
\newcommand{\dist}{\sim}
\newcommand{\distiid}{\overset{\text{iid}}{\dist}}
\newcommand{\distind}{\overset{\text{ind}}{\dist}}

<!-- independence -->
\def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern4mu{#1#2}}}
\newcommand\indep{\protect\mathpalette{\protect\independenT}{\perp}} 

<!-- parametric distributions -->
\newcommand{\distNamed}[1]{{\mathrm{#1}}}
\newcommand{\distNorm}{\mathcal{N}}
\newcommand{\distT}{\mathcal{T}}
\newcommand{\distWish}{\mathcal{W}}
\newcommand{\distInvWish}{\mathcal{IW}}
\newcommand{\distLap}{\distNamed{Lap}}
\newcommand{\distChiSq}{\chi^2}
\newcommand{\distUnif}{\distNamed{Unif}}
\newcommand{\distGam}{\distNamed{Gam}}
\newcommand{\distGum}{\distNamed{Gumbel}}
\newcommand{\distGEV}{\distNamed{GEV}}
\newcommand{\distCat}{\distNamed{Categorical}}
\newcommand{\distInvGam}{\distNamed{InvGam}}
\newcommand{\distPoiss}{\distNamed{Poisson}}
\newcommand{\distExp}{\distNamed{Exp}}
\newcommand{\distNB}{\distNamed{NegBinom}}
\newcommand{\distBeta}{\distNamed{Beta}}
\newcommand{\distBetaPrime}{\distNamed{Beta}'}
\newcommand{\distDir}{\distNamed{Dir}}
\newcommand{\distBinom}{\distNamed{Binom}}
\newcommand{\distMulti}{\distNamed{Multi}}
\newcommand{\distBern}{\distNamed{Bern}}
\newcommand{\distGeom}{\distNamed{Geom}}
\newcommand{\distCauchy}{\distNamed{Cauchy}}
\newcommand{\distVMF}{\distNamed{vMF}}
\newcommand{\distDiscrete}{\distNamed{Discrete}}
\newcommand{\distLKJ}{\distNamed{LKJ}}
\newcommand{\distSkellam}{\distNamed{Skellam}}


<!-- nonparametric distributions -->
\newcommand{\distBeP}{\distNamed{BeP}}
\newcommand{\distDP}{\distNamed{DP}}
\newcommand{\distCRP}{\distNamed{CRP}}
\newcommand{\distPYP}{\distNamed{PY}}
\newcommand{\distGP}{{\distNamed{GP}}} 
\newcommand{\distPP}{\distNamed{PP}}
\newcommand{\distBP}{\distNamed{BP}}
\newcommand{\distBPP}{\distNamed{BPP}}
\newcommand{\distGamP}{\distNamed{\Gamma P}}
\newcommand{\distNGamP}{\distNamed{N\Gamma P}}
\newcommand{\distLP}{\distNamed{LP}}
\newcommand{\distObs}{\distNamed{Obs}}
\newcommand{\distCRM}{\distNamed{CRM}}
\newcommand{\distNCRM}{\distNamed{NCRM}}

<!-- calculus -->
\newcommand{\dee}{\mathrm{d}}
\newcommand{\der}[2]{\frac{\dee #1}{\dee #2}}

<!-- general purpose math -->
\newcommand{\ind}{\mathbb{1}}

\newcommand{\ones}{\boldsymbol{1}}

<!-- divergences -->
\newcommand{\KL}{\operatorname{KL}}
\newcommand{\TV}{\operatorname{TV}}
\newcommand{\Wass}{\operatorname{W}}
\newcommand{\Hell}{\operatorname{H}}
\newcommand{\ELBO}{\operatorname{ELBO}}