PMC

Sample mean and variance of the observed UMI counts of the genes. (A) Expected value vs. variance of sample mean plot. X-axis: Expected value of sample mean; Y-axis: Variance of sample mean. (B) Expected value of sample mean vs. expected value of sample variance plot. X-axis: Expected value of sample mean; Y-axis: Expected value of sample variance. (C) Expected value of sample mean vs. CV of the sample mean plot. X-axis: Expected value of sample mean; Y-axis: CV of sample mean. (D) Expected value of sample mean vs. standard error of sample mean plot. X-axis: Expected value of sample mean; Y-axis: standard error of sample mean. (E) Variance of sample mean vs. expected value of sample variance plot. X-axis: Expected value of variance of sample mean; Y-axis: Expected value of sample variance. (F) CV of sample mean vs. expected value of sample variance. X-axis: CV of sample mean; Y-axis: Expected value of sample variance.

(a) The fitting of sample coefficient of variance from a ketoconazole study (). The solid line is the sample coefficient variance, and dots are the posterior draws of the predicted coefficient of variance. (b) The fitting of sample coefficient of variance from a midazolam study (). The solid line is the sample coefficient variance, and dots are the posterior draws of the predicted coefficient of variance.

Predictions of the variance of S, the number of parasites per square meter, from four models. For each value of the horizontal axis, which is the log₁₀ sample variance of S in all four panels, the black dot falling along the diagonal shows the same value on the vertical axis as a standard of perfect agreement for comparison with the predicted log₁₀ variance of S from each model shown by the red continuous curve. The predicted variance of S is computed from the observed sample mean of S according to the variance function of S derived theoretically for each model using the parameter estimates a, b, c, d, f, g, and ρ estimated independently from other relationships. There is no curve fitting or adjustment of parameters between the sample variance of S (black dots) and the theoretical variance of S (red curve). The red and black points would be superimposed if the model's predicted variance of S matched perfectly the sample variance of S and if there were no sampling variability in the observations. (A) Model 1 assumes that parasite numbers per host P are independent with TL variance function. (B) Model 2 assumes that parasite numbers per host P are independent with negative binomial variance function. (C) Model 3 assumes that parasite numbers P are identical in all hosts with TL variance function. (D) Model 4 assumes that parasite numbers P are identical in all hosts with negative binomial variance function. Only models 3 and 4 predict a variance of S close and linearly related to the observed sample variance of S over the whole range of the observed sample variance of S. All panels have 209 data points. obs., observed; pred., predicted.

DNA methylation variance with age. A) Mean inter-animal mCG variance of cytosines present at ≥20× sequencing depth in every sample (354,522 CG sites) among young and old males (blue distributions) and females (red distributions) relative to density of sites at a given mean variance. mCG variance distribution in old males (mean variance = 0.157774) compared to young males (mean variance = 0.103581) was significantly higher (p = 8.0 × 10–5), while comparison of mCG variance in old females (mean variance = 0.112484) to young females (mean variance = 0.107045) was not significant (p = .35). B) Mean inter-animal mCH variance of cytosines present at ≥20× sequencing depth in every sample (5,577,396 CH sites) among young and old males (blue distributions) and females (red distributions) relative to density of sites at a given mean variance. mCH variance distribution in old males (mean variance = 0.050142) compared to young males (mean variance = 0.034209) was significantly higher (p = 2.9 × 10–5), while comparison of mCH variance in old females (mean variance = 0.038597) to young females (mean variance = 0.033432) was not significant (p = .88).