Table 1. Model selection results for the five models considered.

Models
	Model 1	Model 2	Model 3	Model 4	Model 5
10,000 cells per well
PDE Error (%)	(20.864, 32.123)	(13.943, 23.048)	(21.158, 32.887)	(14.554, 23.934)	(14.219, 23.564)
α 1	—	(−3.456, −0.217) [−1.464]	—	(−3.863, −0.372) [−1.514]	(−2.688, −0.637) [−1.118]
α2 (h−1)	—	(0.091, 0.373) [0.240]	—	(0.084, 0.402) [0.174]	(0.104, 0.341) [0.166]
β1 (μm2 h−1)	(54.396, 289.822) [164.829]	(51.93, 365.923) [203.149]	—	—	(92.394, 326.322) [99.486]
β2 (μm2 h−1)	—	—	(20.608, 979.03) [429.285]	(13.828, 849.614) [307.338]	$(-254.821,1065.03)[-153.593]$
β 3	—	—	—	—	(1.927, 3.286) [3.018]
γ1 (h−1)	(0.045, 0.052) [0.049]	(0.054, 0.063) [0.058]	(0.045, 0.052) [0.049]	(0.053, 0.065) [0.057]	(0.053, 0.062) [0.058]
$\mathbb{P}\left(E_1\right)$	0.00	0.96	0.0	0.07	0.04
$\mathbb{P}\left(E_2\right)$	0.01	0.00	0.0	0.03	0.23
$\mathbb{P}\left(E_3\right)$	0.99	0.04	1.0	0.90	0.73
12,000 cells per well
PDE Error (%)	(15.736, 21.384)	(10.104, 14.547)	(15.23, 21.331)	(9.747, 14.411)	(10.282, 14.783)
α 1	—	(−3.088, −0.854) [−1.619]	—	(−3.055, −0.826) [−1.574]	(−2.403, −1.092) [−1.847]
α2 (h−1)	—	(0.133, 0.307) [0.202]	—	(0.13, 0.303) [0.189]	(0.16, 0.253) [0.220]
β1 (μm2 h−1)	(91.735, 193.201) [141.416]	(117.181, 222.334) [170.212]	—	—	(106.845, 219.685) [169.49]
β2 (μm2 h−1)	—	—	(207.898, 584.976) [423.608]	(194.568, 531.537) [320.266]	(−437.945, −179.991) [−328.306]
β 3	—	—	—	—	(7.306, 9.143) [8.261]
γ1 (h−1)	(0.044, 0.049) [0.046]	(0.055, 0.062) [0.057]	(0.044, 0.048) [0.046]	(0.054, 0.061) [0.057]	(0.054, 0.062) [0.057]
$\mathbb{P}\left(E_1\right)$	0.00	1.00	0.00	0.00	0.16
$\mathbb{P}\left(E_2\right)$	0.00	0.00	0.00	0.00	0.49
$\mathbb{P}\left(E_3\right)$	1.00	0.00	1.00	1.00	0.35
14,000 cells per well
PDE Error (%)	(11.794, 14.811)	(10.147, 14.635)	(10.598, 16.571)	(9.996, 15.573)	(9.9, 17.135)
α 1	—	(−2.858, −0.866) [−1.091]	—	(−2.588, −0.744) [−0.873]	(−2.395, −1.12) [−1.573]
α2 (h−1)	—	(0.199, 0.401) [0.229]	—	(0.19, 0.401) [0.233]	(0.232, 0.361) [0.269]
β1 (μm2 h−1)	(423.353, 689.093) [559.121]	(452.419, 763.335) [624.576]	—	—	(339.505, 753.689) [648.980]
β2 (μm2 h−1)	—	—	(956.516, 2020.74) [1576.910]	(841.97, 2012.11) [1370.458]	$(-903.293,803.306)[-560.316]$
β 3	—	—	—	—	(1.552, 3.66) [3.279]
γ1 (h−1)	(0.047, 0.052) [0.052]	(0.054, 0.061) [0.058]	(0.047, 0.052) [0.049]	(0.052, 0.059) [0.056]	(0.054, 0.061) [0.057]
$\mathbb{P}\left(E_1\right)$	0.05	0.84	0.04	0.01	0.20
$\mathbb{P}\left(E_2\right)$	0.04	0.09	0.01	0.01	0.20
$\mathbb{P}\left(E_3\right)$	0.91	0.07	0.95	0.98	0.60
16,000 cells per well
PDE Error (%)	(10.648, 14.259)	(8.407, 12.702)	(10.217, 15.381)	(8.876, 14.332)	(8.183, 13.768)
α 1	—	$(-2.256,0.022)[-1.024]$	—	(−2.17, −0.1) [−1.203]	(−2.636, −0.449) [−2.034]
α2 (h−1)	—	(0.097, 0.335) [0.180]	—	(0.102, 0.34) [0.213]	(0.218, 0.477) [0.363]
β1 (μm2 h−1)	(382.49, 647.908) [518.476]	(434.293, 727.624) [595.310]	—	—	(380.617, 732.718) [478.344]
β2 (μm2 h−1)	—	—	(808.965, 1581.16) [1068.249]	(728.143, 1549.18) [1126.042]	$(-623.709,183.84)[-400.083]$
β 3	—	—	—	—	(4.582, 7.115) [5.833]
γ1 (h−1)	(0.049, 0.055) [0.052]	(0.056, 0.067) [0.060]	(0.048, 0.054) [0.051]	(0.055, 0.065) [0.059]	(0.052, 0.064) [0.059]
$\mathbb{P}\left(E_1\right)$	0.01	0.92	0.00	0.07	0.15
$\mathbb{P}\left(E_2\right)$	0.00	0.01	0.00	0.00	0.22
$\mathbb{P}\left(E_3\right)$	0.99	0.07	1.00	0.93	0.63
18,000 cells per well
PDE Error (%)	(7.949, 10.907)	(6.609, 8.923)	(8.772, 12.14)	(7.152, 9.74)	(6.663, 10.902)
α 1	—	$(-1.45,0.066)[-0.765]$	—	(−1.436, −0.022) [−0.671]	(−1.173, −0.453) [−0.994]
α2 (h−1)	—	(0.059, 0.236) [0.136]	—	(0.056, 0.207) [0.117]	(0.085, 0.194) [0.140]
β1 (μm2 h−1)	(433.393, 760.833) [565.126]	(470.944, 922.542) [654.164]	—	—	(300.168, 950.728) [653.921]
β2 (μm2 h−1)	—	—	(655.963, 1614.74) [1016.562]	(561.39, 1724.61) [1085.503]	$(-579.707,177.486)[-408.079]$
β 3	—	—	—	—	(4.54, 6.519) [5.066]
γ1 (h−1)	(0.054, 0.061) [0.059]	(0.064, 0.088) [0.070]	(0.053, 0.06) [0.057]	(0.064, 0.09) [0.070]	(0.065, 0.087) [0.069]
$\mathbb{P}\left(E_1\right)$	0.04	0.76	0.00	0.00	0.32
$\mathbb{P}\left(E_2\right)$	0.01	0.11	0.00	0.00	0.07
$\mathbb{P}\left(E_3\right)$	0.95	0.13	1.00	1.00	0.61
20,000 cells per well
PDE Error (%)	(8.76, 11.287)	(7.206, 9.61)	(10.896, 14.895)	(8.211, 11.926)	(7.293, 10.536)
α 1	—	(−4.544, −1.961) [−2.434]	—	(−2.402, −1.721) [−2.068]	(−1.713, −0.891) [−1.014]
α2 (h−1)	—	(0.301, 0.555) [0.340]	—	(0.269, 0.384) [0.320]	(0.15, 0.24) [0.215]
β1 (μm2 h−1)	(401.865, 664.394) [542.045]	(443.875, 852.295) [655.544]	—	—	(506.936, 1251.44) [863.584]
β2 (μm2 h−1)	—	—	(628.934, 1170.63) [880.493]	(627.656, 1461.9) [850.253]	(−1080.17, −433.677) [−747.381]
β 3	—	—	—	—	(1.142, 1.477) [1.316]
γ1 (h−1)	(0.069, 0.077) [0.072]	(0.083, 0.093) [0.088]	(0.072, 0.084) [0.079]	(0.086, 0.099) [0.094]	(0.082, 0.099) [0.085]
$\mathbb{P}\left(E_1\right)$	0.00	0.84	0.00	0.00	0.26
$\mathbb{P}\left(E_2\right)$	0.00	0.09	0.00	0.00	0.09
$\mathbb{P}\left(E_3\right)$	1.00	0.07	1.00	1.00	0.65

Interval estimates, PDE errors, and model selection results for the models in (3)–(6) when applied to the each data set from Jin et al. [13]. The numbers in square brackets give the modes from the kernel density estimates of the corresponding bootstrap sample for the corresponding parameter. The PDE errors are computed using sampled initial conditions. Significance levels for all confidence intervals are 95%. The blue column for each data set highlights the optimal model, and the red text indicates confidence intervals that contain 0.