Table 4 High gene variance is not a good indicator of cell type heterogeneity under the alternative hypothesis of zero-inflated negative binomial, because the variance can be lower under the alternative hypothesis
Alternative hypothesis | Variance under H0 | Variance under HA |
|---|---|---|
Mixture of Poisson | \(\lambda = \sum _{k}\pi _{k}\lambda _{k}\) | \(\sum _{k} \pi _{k} (\lambda _{k}+\lambda _{k}^{2})-(\sum _{k}\pi _{k}\lambda _{k})^{2}\) |
Negative Binomial | λ | \(\frac {\lambda ^{2}}{r} + \lambda \) |
Zero-inflated negative binomial | λ | \((1-\pi _{0})^{2} \left (\frac {\lambda ^{2}}{r} + \lambda \right)\) |