This thesis is the first to apply the novel concept of a parsimonious statistical reservoir model to the accurate prediction of the short-term response of a hydrocarbon reservoir to perturbations in effective stress at well sites from water injection and hydrocarbon production. The inversion for the Statistical Reservoir Model is done by combining multivariate linear regression, a Bayesian Information criterion (BIC) for model optimisation, and Bayesian statistical modelling, to establish which well pairs have statistically significant correlations in monthly flow rate data. The statistical method is tested on real flow rate data from the Gullfaks oil field in the North Sea, and independently verified using the output of a physical reservoir simulation model with known characteristics. The results clearly show that long-range correlations of flow rate at well sites are sensitive to both the present-day stress field and pre-existing fault structures. Significantly spatio-temporally correlated well pairs align with respect to the direction of maximum principal horizontal stress or at preferred angles of ~30°, implying a response in the directions of incipient tensile or shear failure. This confirms that geo-mechanical effects exert a strong control on the reservoir response to fluid injection and withdrawal. A principal component analysis of the regression matrix reveals structures that can be interpreted as hydraulically reactive features, mapping in position and orientation on to the pattern of main faults in the field. These results demonstrate that the Statistical Reservoir Model contains relevant information on the hydraulic structure and geo-mechanical state of the reservoir. It can therefore be applied to improving reservoir description as well as improved short term predictive power. The former will help with longer tem prediction of reservoir response by conventional physical models, and the latter as an independent test of their short-term predictive power.