From noise to models to numbers: Evaluating negative binomial models and parameter estimations in single-cell RNA-seq
Fig 4
E[BIC] shows that a single-sample-based criterion can reliably recover the expected model-selection landscape across sample sizes and telegraph-model regimes. (a) Cartoon illustrating a computational approach to compare the aeBIC (top) with E[BIC] — the expected value of the BIC (bottom). The aeBIC utilizes a single score to select the best model distribution (telegraph, NB or Poisson) given that the ground-truth mRNA distribution is that of the telegraph model. The BIC method assigns a score to each different sample of simulated data from the telegraph model and then all these scores are averaged leading to E[BIC]. (b) The relative error (RE) of aeBIC compared to E[BIC] for two distributions (Poisson and NB) as a function of sample size for 10 parameter sets (see Table A in S1 Text for the values of
and
; ρ is fixed to 15). Error bars show the standard error of the mean. (c) Phase diagram showing the regions of parameter space where the telegraph, NB and Poisson distributions are selected as optimal by the aeBIC, given that the ground-truth mRNA distribution is that of the telegraph model. Here
is the sample size,
is the sum of gene-state switching rates normalised by the degradation rate of mRNA, and
is the fraction time spent in the active state. The fraction of the total parameter space occupied by the region where the NB distribution is optimally selected is shown on the plots. Note that the transcription rate is fixed to
which implies that the maximum mean number of transcripts in the phase plots is 15.