Table 3.

Description of mathematical notations for transcript quantification

Mathematical notations	Descriptions
$r$	read index
$i$	transcript index
$j$	equivalence read classes (equiRC) index
$M$	total number of transcripts
$K$	total number of equivalence read classes (equiRC)
$N$	total number of reads, i.e., sequencing depth
${\tau }_i\left({\tau }_i{}^f,{\tau }_i{}^p,{\tau }_i{}^u\right)$	true read count for isoform $i$,superscripts $f$, $p$, $u$, represent true full-length, partial length, and unique alignment read count respectively
$R^t{}_{ri}$	the event that whether a read $r$ originates from transcript $i$: takes a value of 1 when it happens and 0 otherwise (the realisation value)
$R^{rc}{}_{rj}$	the event that whether a read $r$ matches a equiRC $j$
$R^{rc,t}{}_{rij}$	the event that whether a read that is assigned to equiRC $j$ originates from transcript $i$
$S^t{}_i$	the set of reads that originate from transcript $i$
$S^{rc}{}_j$	the set of reads that are assigned to equiRC $j$
$S^{rc,t}{}_{ij}$	the set of reads in equiRC $j$ being generated from isoform $i$
$T^{rc}{}_j$	the set of transcripts that are compatible with equiRC $j$
$R{C}^t{}_i$	the set of equiRCs which are compatible with transcript $i$
$a_{ij}$	the conditional probability that a read $r$ matches to a equiRC $j$conditioning on the read $r$ originates from transcript $i$
${\theta }_i$	global true relative expression of isoform $i$
$n_{ij}$	unobserved number of reads in equiRC $j$ originate from isoform $i$
$n_j$	number of reads in equiRC $j$
$I^f{}_{ij}\left(I^u{}_{ij}\right)$	an indicator variable takes a value of 1 when reads in read class $j$ that originate from transcript $i$ are full length reads (unique reads) and 0 otherwise

The realisations of these variables are denoted with a prime symbol (′) on top.