Fits the Poisson model's scaling factor (alpha) using the observed relationship between mean-expression and dropout rate.
a numeric matrix of raw UMI counts, columns = samples, rows = genes.
The Poisson model considers each observation to be drawn from a Poisson distribution with parameter:
lambda_ij = m_i * m_j * T * alpha
are the proportion of all molecules detected that are of gene i or in cell j respectively, and T is the total molecules detected across all genes and cells.
This function fits the scaling parameter
which approximates the extent of over-counting of molecules using the observed relationship between mean-expression and dropout rate. Fitting is performed in two steps using maximum-likelihood estimation implemented by mle2 from the statmod package. First, a simplified model which excludes the
factor is fit using multiple starting points in case of poor convergence. Second, the estimated
is used as a starting point to fit the full model.
This procedure improves stability and speed of fitting.
List of output containing: s = observed mean expression of each gene (m_i) p_obs = observed gene-specific dropout rate p_exp = model-based gene-specific dropout rate p_exp_var = model-based variance of gene-specific dropout rate alpha = final fit scaling parameter alpha_basic = initial fit scaling parameter from simplified model lambdas = matrix of calculated lambda for each expression value (same dimensions as input matrix).
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