I am running a chain of Monte Carlo simulations to estimate uncertainty in some model estimates (which are derived from a series of estimates). An important variables used in one of the steps is a sample proportion, which sometimes is near or at zero successes (e.g., 0 out of 20 fish were of hatchery-origin).
Here is a simplified example of my problem.
Simulate sample proportions and estimate confidence interval from the distribution
simulated_proportions = rbinom(n = 1000, size = 20, prob = 0) / 20 quantile(simulated_proportions, probs = c(0.5, 0.025, 0.975)) 50% 2.5% 97.5% 0 0 0
Compare simulated confidence intervals to Wilson-Score approximation
library(Hmisc) binconf(x = 0, n = 20, alpha = 0.05, method = "wilson") PointEst Lower Upper 0 0 0.1611252
My simulated data underestimate potential uncertainty in the sample proportion. It is important that uncertainty in this step is included in this step of the MC simulations.
Any advice on how to address this problem?