We provide an axiomatic approach to a belief formation process in an informational environment

characterized by limited, heterogenous and differently precise information. For a list of previously

observed cases an agent needs to express her belief by assigning probabilities to possible outcomes.

Different numbers of observations of a particular case give rise to varying precision levels associated

to the pieces of information. Different precise information affects the cautiousness and confidence

with which agents form estimations. We modify the Concatenation axiom introduced in Billot,

Gilboa, Samet and Schmeidler (BGSS) (Econometrica, 2005) in a way to capture the impact of

precision and its related perceptional effects, while still keeping its normative appealing spirit. We

obtain a representation of a belief as a weighted sum of estimates induced by past cases. The

estimates are affected by cautiousness and confidence considerations depending on the precision

of the underlying observed information, which generalizes BGSS. The weights are determined by

frequencies of the observed cases and their similarities with the problem under consideration.