In this paper, we develop a unified Bayesian approach that enables the prediction of binary random events and random scalar fields from heterogeneous data collected by mobile sensor networks with different detectors and sensors. The heterogeneous uncertainties such as different false detection rates and measurement noises are taken into account. This proposed unified approach exploits the statistical correlations among heterogeneous random events and random fields via their latent random variables which are modeled by a Gaussian Markov random field. The statistical inference based on Gaussian approximation is then provided in order to predict the random events and/or scalar fields. The fully Bayesian approach based on the integrated nested Laplace approximation is also proposed to deal with the case where model parameters are not known a priori. Simulation results demonstrate the correctness and usefulness of the proposed approaches.