Fig. 1

Model outline. BEDwARS takes as input the bulk expression profiles (\(X\)) as well as the reference signatures of individual cell types (\({S}^{r}\)). BEDwARS models bulk profiles (\(X\)) as combinations of “true” but unknown signatures (\(S\)) of cell types mixed in unknown proportions (\(W\)) and estimates both \(S\) and \(W\) from data. The true signatures are assumed to be similar to the reference signatures and differences between them are assumed to be normally distributed with mean zero and variance proportional to the reference gene expression (\({S}_{gc}^{r}\)). The constant of proportionality is a cell-type specific parameter (\({\sigma }_{c}\)) that allows for the degree of differences to vary across the cell types. The unknown cell type proportions (\(W\)) are assumed to follow a Dirichlet distribution. Maximum a posteriori estimation is used to find the cell type proportions and signatures based on the data