u	Measured cell transcriptome ($\in {\mathbb{R}}^N$)
Ω	Embedding space to which u is mapped
X∈Ω	Cell transcriptome after dimensionality reduction
Ps(x)	Probability density of singlets (in Ω)
PD(x)	Probability density of true doublets (in Ω)
P′D(x)	Probability density of simulated doublets (in Ω)
P obs (x)	Probability density of observed transcriptomes (in Ω)
ρ	Fraction of observed transcriptomes that are doublets
$\widehat{\rho }$	Prior belief in the value of ρ
Mobs	Total number observed transcriptomes
M D	Total number simulated doublets
r	MD/Mobs
k	Number of nearest neighbors for KNN classification
k d	Number of nearest neighbors to x that are simulated doublets
k obs	Number of nearest neighbors to x that are observed transcriptomes
q(x)	The binomial proportion of nearest neighbors that are simulated doublets
$\mathcal{L}(x)$	The Likelihood that a transcriptome x is a doublet
〈·〉	Expectation value of an estimator
SE[·]	The standard error of the estimator