FIG. 3: Q-Q plots of the Method-1 conditional reference posterior (left) and the Method-2 marginal reference posterior (right) versus the standard normal distribution. The reference posterior quan- tiles have been recentered (see text). N$_{R}$ is the number of measurement replications and n$_{tot}$ is the observed number of events summed over all replications. posterior for σ are plotted against standard normal quantiles. The posterior quantiles Q$_{π}$ are recentered according to ˜ Q$_{π}$ = ( Q$_{π}$ − 〈 σ 〉 ) / Δ σ , where the posterior mean 〈 σ 〉 and stan- dard deviation Δ σ are numerically estimated. For Method 1 we set the true values of σ , ϵ , and µ to 1. We then randomly generate a sequence of 100 independent measurements from the probability mass function (16) and use the subsequences with N$_{R}$ = 1, 10, and 100 to produce the curves in the left panel. For Method 2 we set the true value of σ to 1 and give the priors for ϵ and µ each a mean of 1 and a coefficient of variation of 20%. Measurements are then generated from the probability mass function (28) in order to compute the curves in the right panel. Both panels clearly show that the respective reference posteriors approach a Gaussian shape as the number of measurement replications increases. Given the almost negligible difference between Method-1 and 2 posteriors exhibited in Fig. 2, and the fact that our analytical results for Method 1 are computationally more tractable than those for Method 2, our considerations in the remainder of this section will focus exclusively on Method 1. Among the reference prior properties listed in Sec. II, the ones of generality, invariance, and coherence are true by construction. The property of sampling consistency needs more elaboration however, since Bayesian inferences do not generally coincide with exact fre- 20