On conservativeness of posterior density fusion

The paper deals with information fusion in a decentralised estimation problem. Supposing the dependence of input information pieces is unknown, conservative fusion requires to not overestimate the quality of the fusion output. The classical and Bayesian perspectives are reviewed and the fusion performed by a weighted geometric mean of the input posterior probability densities is inspected. The paper proposes to use two concepts of conservativeness, the observed and expected ones. The provided examples show that in a general case, the used fusion rule does not ensure the fused density to be conservative.