Figure 9.

(a) The likelihood function $\mathcal{L}\left(E_d|N_0\right)$ in Eq. 20 for the endpoint dilution assay and the corresponding maximal likelihood, RM, and SK estimates given simulated data generated with N₀ = 10⁶, Q = 1, D = 10, and d_max = 10. The estimates for maximal likelihood $\left({\hat{N}}_0=1.33\times {10}^6\right)$, RM $\left({\hat{N}}_0=2.51\times {10}^6\right)$, and SK $\left({\hat{N}}_0=2.51\times {10}^6\right)$ all overestimate N₀, but the smaller relative error of the MLE is an improvement on the errors of the existing two methods. (b) The likelihood functions $\mathcal{L}\left(P_{d,t}|N_0\right)$ and $\mathcal{L}\left(E_d|N_0\right)$ for the plaque and endpoint dilution assays, respectively, are shown, given simulated data. The data were generated with the parameters N₀ = 10⁶, M = 10⁵, Q = 1, D = 10^1/4, d_max = 30, and a “countable plaque threshold” of 150. The plaque assay likelihood is concentrated close to the true N₀ value, whereas the endpoint dilution likelihood is far more spread out and overestimates N₀. This direct quantitative comparison can inform an experimentalist when choosing between the two methods. To see this figure in color, go online.