# Bayesian Modeling of Traffic Accident Rates in Poland Based on Weather Conditions
## 1 Introduction
Temperature also influences traffic safety, with studies linking rising temperatures to an increased risk of crashes [23; 24], particularly when extreme heat impairs driver concentration or encourages riskier behavior [25]. Conversely, subzero temperatures do not necessarily pose a direct threat unless they result in ice formation and snow accumulation [22]. Driver behavior adapts to adverse weather conditions, with reduced speeds and increased following distances observed during rainfall events, effects that intensify with precipitation severity [26]. Risk perception among drivers varies by weather condition and vehicle type, but among all, snow-covered roads pose the highest risk [27]. The complex interrelationships between weather variables, driver behavior, regional factors, and accident patterns underscore advanced modeling approaches. Researchers have applied various methodological frameworks to better understand these dynamics. Time series models have proven particularly valuable for capturing temporal dependencies in accident data [28; 29]. In particular, ARIMA (Autoregressive Integrated Moving Average) models were used to establish associations between weather factors and trauma occurrences from collisions [30]. [PERSON] et al. [24] employed a Generalized Additive Model (GAM) with a Poisson distribution combined with meta-analysis techniques to identify temperature thresholds above which traffic accidents significantly increased in urban areas. Multivariate modeling approaches have enabled the simultaneous modeling of multiple factors. [PERSON] et al. [31] proposed multivariate safety performance functions with multiple regression links to model both the frequency and severity of collisions in relation to weather variables and exposure proxies, achieving high predictive precision. Poisson regression models have been widely applied to accident count data, given their suitability for discrete, non-negative outcomes. [PERSON] et al. [9] employed this approach to decompose the contribution of various factors--including randomness, exposure, and weather--to variations in road accident counts. The spatial dimension of weather-accident relationships has been addressed through innovative methodological methods. [PERSON] et al. [32] introduced a weather radar approach to analyze rainfall impacts on urban accidents, providing superior spatial and temporal resolution compared to traditional station-based analyses. This methodology proved generally more effective, highlighting the importance of contextual factors in methodological selection. Risk assessment frameworks have also been developed to quantify the relative hazards associated with specific weather conditions. [PERSON] et al. [33] employed Palm probability theory--derived from random point processes--to estimate the relative accident risks across different road weather conditions. This approach revealed particularly elevated risks during icy rain and on slippery road surfaces, with counterintuitive findings regarding the vulnerability of different road types during adverse conditions. Meta-analytical approaches have provided valuable integration of diverse research findings. [PERSON] et al. [34] used multidimensional comparative analysis to analyze traffic safety and road infrastructure development indicators between different regions. [PERSON] et al. [19] conducted a meta-analysis on the effects of adverse weather on traffic crashes to generalize research findings. This way, they excluded local phenomena and found the generalized influence of the different factors. [PERSON] et al. [35] highlighted the potential for real-time traffic and weather data to enable not only more precise estimation of individual parameter effects but also identification of complex interaction effects between traffic and weather variables. This increasing data granularity supports the development of predictive models with greater temporal and spatial specificity.