Intersections are among the most dangerous roadway facilities due to the complex traffic conflicting movements and frequent stop-and-go traffic. However, previous intersection safety analyses were conducted based on static and highly aggregated data (e.g., annual average daily traffic (AADT), annual crash frequency). These aggregated data may result in unreliable findings simply because they are averages and cannot represent the real conditions at the time of crash occurrence. This study attempts to investigate the relationship between crash occurrence at signalized intersections and real-time traffic, signal timing, and weather characteristics based on 23 signalized intersections in Central Florida. The intersection and intersection-related crashes were collected and then divided into two types, i.e., within intersection crashes and intersection entrance crashes. Bayesian conditional logistic models were developed for these two kinds of crashes, respectively. For the within intersection models, the model results showed that the through volume from "A" approach (the traveling approach of at-fault vehicle), the left turn volume from "B" approach (near-side crossing approach), and the overall average flow ratio (OAFR) from "D" approach (far-side crossing approach), were found to have significant positive effects on the odds of crash occurrence. Moreover, the increased adaptability for the left turn signal timing of "B" approach and more priority for "A" approach could significantly decrease the odds of crash occurrence. For the intersection entrance models, average speed was found to have significant negative effect on the odds of crash occurrence. The longer average green time and longer average waiting time for the left turn phase, higher green ratio for the through phase, and higher adaptability for the through phase can significantly improve the safety performance of intersection entrance area. In addition, the average queue length on the through lanes was found to have positive effect on the odds of crash occurrence. These results are important in real-time safety applications at signalized intersections in the context of proactive traffic management.