Ensuring the safety of autonomous vehicle (AV) relies on accurate prediction of error occurrences in its perception system. Due to the inter-stage functional dependence, the error occurred at a certain stage may be propagated to the following stage and generate extra errors. To quantify the error propagation, this paper adopts the physics-based simulation, which enables fault injection at different stages of an AV perception system to generate error event data for error propagation modeling. A multi -stage Hawkes process (MSHP) is proposed to predict the error occurrences in each stage, with error propagation represented as a latent triggering mechanism. With explicitly considering the error propagation mechanism, the proposed outperforms benchmark methods in predicting error occurrence in a physics-based simulation of a multistage AV perception system. The proposed two-step likelihood-based algorithm accurately estimates the model coefficients in a numerical simulation case study.