This study establishes a mathematical model that can represent the conflicting effects of two pedestrian streams with an oblique intersecting angle in a large crowd. In a previous study, a controlled experiment in which two streams of pedestrians were asked to walk in designated directions was used to model the bi-directional pedestrian stream of certain intersecting angles. In this study, we revisit that problem and apply the Bayesian inference approach to calibrate an improved model with the controlled experiment data. We also collected pedestrian movement data from a busy crosswalk using a video observation approach. The two sets of data are used separately to calibrate our proposed model. With the calibrated model, we study the relationship between speed, density, and flow in both the reference and conflicting streams, and predict how these factors affect the interactions of moving pedestrian streams. We find that the speed of one stream not only decreases with its total density, but it also decreases with the ratio of its flow in relation to the total flow, i.e., the speed of the pedestrians decreases if their stream changes from the major to the minor stream. We also observe that the maximum disruption induced by pedestrian flow from an intersecting angle occurs when the angle is near 135.