Confidence interval of 0 observations with Poisson distribution

https://stats.stackexchange.com/questions/427019/confidence-interval-for-mean-of-poisson-with-only-zero-counts

Excellent answer in this link about the confidence interval when only 0 observations are available for a Poisson distribution.

 Here is an alternative using Bayesian MCMC with uniform distribution.

 This is surprising how close are the estimates !

library(HelpersMG)
u <- NULL

for (l in 1:30) {
  val <- rep(0, l)
  prior <- data.frame(Density="dunif",
                      Prior1=0, Prior2=10,
                      SDProp=1,
                      Min=0, Max=10,
                      Init=0.01, row.names = "lambda")
  mcmc_run <- MHalgoGen(n.iter=100000, parameters=prior, data=val, adaptive = TRUE,
                        likelihood=dpoisx, n.chains=1, n.adapt=10000, thin=10, trace=FALSE)
  u <- c(u, quantile(mcmc_run$resultMCMC$"1"[, "lambda"], probs=0.95))
}

plot_errbar(1:30, rep(0, 30), y.minus=rep(0, 30), y.plus = u, las=1, bty="n",
            xlab="Number of observations", ylab="95% confidence interval", ylim=c(0, 3))

points(1:30, qgamma(.95, shape = 1, rate = 1:30), pch="X")
points(1:30, -log(.05)/(1:30), pch="+", col="red")

legend(x = "topright", pch=c("+", "X", "+"), col=c("black", "black", "red"),
       legend = c("Bayesian MCMC", "Bayes theorem", "Frequentist"))


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