content_image/365090.jpg content_image/365088.jpg
<img src='content_image/365090.jpg'>

posterior has the form: 

and the reference prior π$_{R}$ ( σ, ϵ, µ ) is calculated from the combined likelihood for the N$_{R}$ measurements; it can also be calculated from a single one of these likelihood functions, since it follows from their constructive definition (14) that reference priors are independent of sample size. For Method 1 the prior is given by the product of Eqs. (17) and (25), and the likelihood component f ( n | σ, ϵ, µ ) by Eq. (16). Replicating the measurement N$_{R}$ times is then equivalent to making a single measurement with a Poisson likelihood whose mean is N$_{R}$ times the original mean, and whose observation is the sum of the N$_{R}$ original obser- vations n$_{i}$ . This property of Poisson measurements simplifies the calculations considerably. For Method 2 the prior is given by Eq. (30) and the likelihood by Eq. (28). In this case no simplification obtains when considering multiple replications, and numerical calculations must use explicitly the full product of likelihood functions. Figure 3 illustrates the calcu- lations with the help of so-called Q-Q plots, where recentered quantiles from the reference 

<img src='content_image/365088.jpg'>

