Bartlett’s paradox has been taken to imply that using improper priors results in Bayes factors that are not well defined, preventing model comparison in this case. We use well understood principles underlying what is already common practice, to demonstrate that this implication is not true for some improper priors, such as the Shrinkage prior due to Stein (1956). While this result would appear to expand the class of priors that may be used for computing posterior odds, we warn against the straightforward use of these priors. Highlighting the role of the prior measure in the behaviour of Bayes factors, we demonstrate pathologies in the prior measures for these improper priors. Using this discussion, we then propose a method of employing such priors by setting rules on the rate of diffusion of prior certainty.

Several closely-spaced phosphorite beds stand out at the Albian–Cenomanian transition in the mid-Cretaceous transgressive succession at the northeastern margin of the Holy Cross Mountains, central Poland. They form a distinctive condensed interval of considerable stratigraphical, palaeontological, and economic value. Here, we correlate the classical section at Annopol with a recently investigated section at Chałupki. We propose a new stratigraphic interpretation of the phosphorite interval, based on lithological correlations, Rare Earth Elements and Yttrium (REE+Y) signatures of phosphorites, age-diagnostic macrofossils, and sequence stratigraphic patterns. This interval has long been considered as exclusively Albian in age. However, new macrofossil data allow us to assign the higher phosphorite levels at Annopol and Chałupki, which were the primary target for the phosphate mining, to the lower Cenomanian. In terms of sequence stratigraphy, the phosphorite interval encompasses the depositional sequence DS Al 8 and the Lowstand System Tract of the successive DS Al/Ce 1 sequence. The proposed correlation suggests that lowstand reworking during the Albian–Cenomanian boundary interval played an important role in concentrating the phosphatic clasts and nodules to exploitable stratiform accumulations. Our conclusions are pertinent to regional studies, assessments of natural resources (in view of the recent interest in REE content of the phosphorites), and dating of the fossil assemblages preserved in the phosphorite interval. On a broader scale, they add to our understanding of the formation of stratiform phosphorite deposits.