Abstract
In this paper, we present some Bayesian results about the stability under products of the concepts of sufficiency, minimal sufficiency and completeness, extending frequentist results by Chacón et al. [2006. A note on minimal sufficiency. Statist. Sinica 16 (1), 7–14] and Landers and Rogge [1976. A note on completeness, Scand. J. Statist. 3, 139]. These results are used to throw some light on the study of the relationship between minimal sufficiency and invariance, a question that, in a classical setting, has been considered in the first of the former papers and in Hall et al. [1965. The relationship between sufficiency and invariance with applications in sequential analysis. Ann. Math. Statist. 36, 575–614].
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