Table 1 Estimation of model parameters \( \hat{\alpha}\ and\ \hat{\beta} \) under different α and β with fixed number of cells, prct, s, and gene number = 15,000. Comparing with the noise model in Eq. 9, we have obtained fairly low RMSE in each condition

1,000

10

2

0

1

0.0003 ± 0.0002

1.0293 ± 0.0014

0.0074 ± 0.0006

0.044 ± 0.010

1.2

0.0004 ± 0.0003

1.2187 ± 0.0024

0.0047 ± 0.0006

0.066 ± 0.020

1.5

0.0007 ± 0.0004

1.5032 ± 0.0039

0.0028 ± 0.0007

0.091 ± 0.019

0.15

1

0.1557 ± 0.0005

1.0116 ± 0.0009

0.0047 ± 0.0003

0.049 ± 0.008

1.2

0.1562 ± 0.0007

1.1965 ± 0.0020

0.0038 ± 0.0004

0.030 ± 0.004

1.5

0.1569 ± 0.0007

1.4756 ± 0.0047

0.0043 ± 0.0006

0.017 ± 0.001

0.5

1

0.5146 ± 0.0013

1.0020 ± 0.0010

0.0038 ± 0.0004

0.060 ± 0.006

1.2

0.5161 ± 0.0011

1.1837 ± 0.0023

0.0039 ± 0.0003

0.047 ± 0.006

1.5

0.5187 ± 0.0016

1.4561 ± 0.0045

0.0054 ± 0.0005

0.030 ± 0.004