a, Illustration of the two-state model of transcription. The promoter can be in an ON or OFF state and converts from OFF to ON with a rate kon, and from ON to OFF with rate koff. In the ON state, RNAs are transcribed with rate ksyn and degraded with rate deg. See Supplementary Methods. b, Derivation of a confidence interval for a simulated set of observations with a given burst frequency = 0.5 (n = 200 simulated observations). The quadratic function shown in blue is a transformed version of the log-likelihood as a function of burst frequency, in which the most likely parameter value has a likelihood of 0. Standard theory for likelihood methods gives a cut off value of 1.92 for a 95% confidence interval (solid red line), which can then be traced down to their corresponding value on the x axis (dashed red lines) to derive a confidence interval. The true value, shown as a green dot, is within the confidence interval. c, Goodness-of-fit test for 7,382 genes on the C57 allele of the fibroblast cells (from molecular level input data). The histogram shows the mean expression levels of genes with a good (green) or bad (red) fit (Supplementary Methods). d, A scatter plot of the Akaike information criterion (AIC) for the inference obtain from molecule (UMIs) and RPKM values. The green line denotes y = x. e, f, Scatter plot of the burst frequency and size obtained from inference procedure based on either molecules (UMIs) or RPKM values. g, Scatter plot of mean expression against inferred burst frequency for all genes in fibroblasts. Red line denotes spline fitted to data. h, Scatter plot of mean expression against inferred burst size for all genes in fibroblasts. Red line denotes spline fitted to data. Data in g and h are from the CAST allele. i, Scatterplot of the percentage of biallelic to silent cells for 10,727 genes, in fibroblasts. The genes are located on the expected curve under the independence model (see Supplementary Methods and ref. 12 for details).