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We consider a bandwidth-constrained distributed parameter estimation problem, where each sensor makes a noisy observation of an unknown random source . Each sensor is unaware of 's prior distribution and the actual dynamic range of its observation, and simply assumes that its observation is limited to a finite interval [ ]. Each sensor quantizes its observation using a multi-bit uniform quantizer, where the quantization step size is chosen according to . Sensors send their quantized observations to a fusion center (FC), that is tasked with estimating based on the received data from the sensors. We derive the Bayesian Fisher information, which is the inverse of the Bayesian Cramer-Rao lower bound, for two types of random , namely Gaussian and Laplacian . To quantify the amount of information loss on when the FC uses the quantized observation for estimating , due to both limited dynamic …