Standard practice in analyzing data from different types of experiments is to treat data from each type separately.  By borrowing strength across multiple sources, an integrated analysis can produce better results. Careful adjustments need to be made to incorporate the systematic differences among various experiments. To this end, some Bayesian hierarchical Gaussian process models (BHGP) are proposed. The heterogeneity among different sources is accounted for by performing flexible location and scale adjustments. The approach tends to produce prediction closer to that from the high-accuracy experiment. The Bayesian computations are aided by the use of Markov chain Monte Carlo and Sample Average Approximation algorithms. The proposed method is illustrated with two examples: one with detailed and approximate finite elements simulations for mechanical material design and the other with  physical and computer experiments. The modeling problem also leads to the construction of a novel class of Latin hypercube designs to accommodate experiments at two levels of accuracy. (Based on joint work with Professor Zhiguang Qian, U. of Wisconsin, Madison.)