By Campbell Bonner
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Indeed, for any sample size n and number of replicates k, I {pθ |Mnk } = nI {pθ |Mk }. Note, however, that Theorem 4 requires x to be a random sample from the assumed model. If the model entails dependence between the observations (as in time series, or in spatial models) the reference prior may well depend on the sample size; see, for example, Berger and Yang (1994), and Berger et al. (2001). The possible dependence of the reference prior on the sample size and, more generally, on the design of the experiment highlights the fact that a reference prior is not a description of (personal) prior beliefs, but a possible consensus prior for a particular problem of scientific inference.