# Bayesian Modeling of Traffic Accident Rates in Poland Based on Weather Conditions
## 1 Introduction
Many of the described modeling approaches face limitations in their ability to fully account for uncertainty, incorporate prior knowledge, and represent complex hierarchical or spatio-temporal structures. They often rely on restrictive assumptions and lack the flexibility needed to capture nonlinear interactions. These limitations underscore the rationale for employing Bayesian statistical frameworks, which offer a coherent probabilistic foundation for addressing such complexities. By incorporating prior information, quantifying uncertainty, and updating beliefs as new data become available, they effectively capture hierarchical structures, spatial and temporal dependencies, and intricate parameter interactions [36]. Bayesian hierarchical models have proven particularly effective in addressing spatial and temporal dependencies in accident data [37]. By pooling information across different locations or time periods, these models enhance estimation precision, especially in data-sparse areas. Similarly, Bayesian network models have been employed to represent the complex causal relationships between various accident-contributing factors [38]. Recent studies reinforce the growing value of Bayesian methods, particularly in weather-related accident analysis. First, they effectively handle the inherent variability and uncertainty in both accident occurrences and weather measurements. Second, they allow for the integration of prior information from past studies or expert knowledge, which is particularly valuable when dealing with complex weather-accident relationships. Third, they provide a natural framework for modeling hierarchical structures, such as accidents nested within geographical regions or time periods [39]. [PERSON] et al. [40] proposed a Bayesian bivariate conditional autoregressive model that jointly analyzes daytime and nighttime crash frequencies while accounting for spatial correlations across traffic analysis zones. Their findings reveal significant spatial effects and high correlation between crash periods,with key predictors including land use and traffic exposure. [PERSON] et al. [41] expanded this perspective by developing a Bayesian spatio-temporal model that captures not only the main effects but also interactions between road geometry and weather factors, such as wind-speed-slope and precipitation-curve combinations, demonstrating their impact on crash risk. Meanwhile, [PERSON] et al. [42] introduced a Bayesian multivariate spatio-temporal interaction framework for ranking hazardous sites based on severity-weighted crash frequencies, showing that models incorporating spatial and temporal dependencies outperform simpler alternatives. [PERSON] [43, 44] developed a Bayesian logistic regression model for classifying accident severity, incorporating various informative priors--including method of moments, maximum likelihood estimation, and two-stage Bayesian updating--alongside a novel Boot prior proposal. Results indicated that models trained on balanced datasets outperformed those trained on unbalanced data, with the two-stage Bayesian updating and Boot prior models achieving the highest classification accuracy. Additionally, the research explored spatial and temporal aspects of Bayesian modeling, where priors were derived from road-specific historical data or the latest available accident records. These findings underscore the importance of prior selection in Bayesian models and their adaptability for analyzing accident risks in both spatial and temporal contexts. The present study aims to address this research gap by developing a comprehensive Bayesian model for analyzing the relationship between weather conditions and traffic accident rates across Poland. By leveraging national-scale data and accounting for spatial and temporal dependencies, this research seeks to provide a more nuanced understanding of how specific weather and socioeconomic parameters influence accident risk in different regions of Poland.