# Bayesian Modeling of Traffic Accident Rates in Poland Based on Weather Conditions
## 4 Conclusions  
This study investigated the relationship between weather conditions, socioeconomic factors, and traffic accident counts in Poland. Bayesian Poisson regression models were employed across two temporal and spatial scales. The first set of models focused on yearly accident counts at the county level. Model 1, which included only socioeconomic predictors, revealed that passenger car ownership had a strong positive association with accident frequency, while population density showed a modest positive effect. This aligns with the well-established principle of traffic exposure, a fundamental concept in traffic safety research [9]. Road density exhibited a negative effect, suggesting that better-developed road networks may contribute to accident reduction. This finding is consistent with literature on the benefits of \"forgiving\" and thoughtfully designed infrastructure, which can mitigate driver error even in areas with high traffic volumes [17; 18]. Posterior predictive checks indicated that the model captured the central tendency of the data well, though some underprediction occurred in counties with higher accident counts. Model 2 extended this framework by incorporating weather variables alongside socioeconomic predictors. While the socioeconomic effects remained stable--confirming the robustness of those associations--weather-related variables added explanatory power. Specifically, mean humidity had a positive effect on accident counts, while both mean temperature and total precipitation had negative effects. The seemingly counterintuitive negative effects of temperature and precipitation at the annual level may reflect broader climate patterns rather than event-specific risks. Counties with higher average annual temperatures and more precipitation may experience fewer days with highly hazardous conditions, which are known to significantly increase collision risk [21; 22]. The positive association with humidity could be a proxy for conditions with reduced visibility, such as fog or mist, which are known hazards. The inclusion of weather factors improved model fit, particularly in terms of predictive accuracy across counties with mid-to-high accident frequencies. The weekly nationwide analysis was conducted using Models 3 and 4. Model 3, which considered only weather variables, identified temperature as having a strong positive effect, with humidity also contributing positively, and precipitation showing a slight negative effect. The positive effect of temperature at the weekly scale, in contrast to the yearly finding, is highly consistent with international studies that link short-term temperature increases and heatwaves to a higher risk of crashes [24; 25]. The slight negative effect of precipitation, while counterintuitive, can be explained by adaptive driver behavior; research has shown that drivers often reduce speeds and increase following distances during rainfall [26]. While the model captured overall patterns reasonably well, discrepancies were observed \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Model** & **Rank** & **ELPD-WAIC** & **p-WAIC** & **ELPD Diff** & **Weight** & **SE** & **dSE** \\ \hline Model 4 & 0 & \(-\)1941.50 & 72.26 & 0.00 & 0.64 & 115.10 & 0.00 \\ Model 3 & 1 & \(-\)2019.21 & 51.29 & 77.70 & 0.36 & 105.12 & 43.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of nationwide models based on WAIC criterion for accident count prediction. mostly in the middle range of accident counts, suggesting room for refinement. Model 4 combined weather and socioeconomic predictors at the weekly scale. This integrated model showed improved predictive performance across most of the accident frequency range. The effects of individual predictors were consistent with earlier models: socioeconomic variables retained their expected directional effects, and weather variables mirrored those in Model 3. Posterior predictive checks demonstrated that Model 4 achieved the best alignment between observed and predicted accident counts.