This study develops a real-time framework for estimating pedestrian crash risk at signalized intersections under heterogeneous, non-lane-based traffic. Existing approaches often assume linear relationships between covariates and parameters, oversimplifying the complex, non-monotonic interactions among different road users. To overcome this, the framework introduces a non-linear link function within a Bayesian generalized extreme value (GEV) structure to capture traffic variability more accurately. The framework applies extreme value theory through the block maxima approach using post-encroachment time as a surrogate safety measure. A hierarchical Bayesian model incorporating both linear and non-linear link functions into GEV parameters is estimated using Markov Chain Monte Carlo simulation. It also introduces a behavior-normalized Modified Crash Risk (MRC) formula to account for pedestrians' habitual risk-taking behavior. Seven Bayesian hierarchical models were developed and compared using deviance information criterion. Models employing non-linear link functions for the location and scale parameters significantly outperformed their linear counterparts. The results revealed that pedestrian speed has a negative relationship with crash risk, while flow and speed of motorized vehicles, pedestrian flow, and non-motorized vehicles conflicting speed contribute positively. The MRC formulation reduced overestimation and provided crash predictions with 93% confidence. The integration of non-linear link functions enhances model flexibility, capturing the non-linear nature of traffic extremes. The proposed MRC metric aligns crash risk estimates with real-world pedestrian behavior in mixed-traffic environments. This framework offers a practical analytical tool for traffic engineers and planners to design adaptive signal control and pedestrian safety interventions before crashes occur.

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