# Analyzing Parking Demand Characteristics Using a Bayesian Model Averaging
## 4 Experiments and Results
### BMA Results  
After fitting the candidate models, the log-likelihood can be obtained according to the given data. Then, AIC and BIC can be calculated, and the posterior model probability is calculated using Equation (7). The results are summarized in Table 5. Note that a higher posterior model probability indicates superior fitting performance for parking duration, while the values equal to 0 indicate that they are extremely small, specifically less than 0.001. For the parking duration of temporary users, the log-normal distribution shows the best performance in describing the characteristics of parking duration, since it has the highest posterior model probability with a value of 0.910. However, normal distribution displays the worst fitting performance in the parking duration modeling, attributable to an exceptionally low posterior model probability (i.e., below 0.001), the minimum log-likelihood (with a value of \(-3710.85\)), and the maximum AIC and BIC values (measuring 7425.69 and 7436.20, respectively). Furthermore, GEV distribution is a viable option for characterizing parking duration features, exhibiting a posterior model probability of 0.090. According to the parking duration of long-term users, GIGMM obtains the maximum posterior model probability with a value of 0.897, indicating that GIGMM is the best model for depicting the characteristics of parking duration. In addition, it is noteworthy that multiple models exhibit substantial posterior model probabilities. The LoganMM model, with a posterior model probability of 0.103, is also a suitable choice for modeling parking duration among long-term users. This indicates that both GIGMM and LoganMM are viable options for modeling parking duration data (the values of posterior model probability are \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Distribution** & **Parameter** & **Estimate** & **Distribution** & **Parameter** & **Estimate** \\ \hline \multirow{3}{*}{GauMM} & \((\omega_{1},\omega_{2})\) & (0.273, 0.727) & \multirow{3}{*}{WeiMM} & \((\omega_{1},\omega_{2})\) & (0.256, 0.744) \\  & \((\mu_{1},\mu_{2})\) & (1.890, 9.406) & & (\(\alpha_{1},\alpha_{2})\) & (10.843, 0.943) \\  & \((\sigma_{1},\sigma_{2})\) & (1.128, 7.278) & & (\(\beta_{1},\beta_{2})\) & (9.044, 6.710) \\ \hline \multirow{3}{*}{LognMM} & \((\omega_{1},\omega_{2})\) & (0.283, 0.717) & \multirow{3}{*}{LogIM} & \((\omega_{1},\omega_{2})\) & (0.298, 0.702) \\  & \((\mu_{1},\mu_{2})\) & (2.171, 1.298) & & (\(\mu_{1},\mu_{2})\) & (2.172, 1.299) \\  & \((\sigma_{1},\sigma_{2})\) & (0.107, 1.163) & & (\(\sigma_{1},\sigma_{2})\) & (0.068, 0.971) \\ \hline \multirow{3}{*}{GamMM} & \((\omega_{1},\omega_{2})\) & (0.248, 0.752) & \multirow{3}{*}{GIGMM} & \((\omega_{1},\omega_{2})\) & (0.271, 0.729) \\  & \((\alpha_{1},\alpha_{2})\) & (87.373, 0.982) & & (\(\mu_{1},\mu_{2})\) & (8.729, 6.816) \\ \cline{1-1}  & \((\beta_{1},\beta_{2})\) & (0.100, 7.007) & & (\(\sigma_{1},\sigma_{2})\) & (0.111, 1.548) \\ \cline{1-1} \cline{2-6}  & & & & (\(\
u_{1},\
u_{2})\) & (46.972, 0.263) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter estimation results of candidate models for long-term users. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Distribution** & **Parameter** & **Estimate** & **Distribution** & **Parameter** & **Estimate** \\ \hline \multirow{3}{*}{Normal} & \(\mu\) & 2.683 & \multirow{3}{*}{Log-logistic} & \(\mu\) & 0.430 \\  & \(\sigma\) & 2.844 & & \(\sigma\) & 0.618 \\ \hline \multirow{2}{*}{Log-normal} & \(\mu\) & 0.466 & \multirow{3}{*}{Burr} & \(\alpha\) & 0.839 \\  & \(\sigma\) & 1.031 & & \(\beta\) & 2.233 \\ \hline \multirow{2}{*}{Gamma} & \(\alpha\) & 1.097 & \multirow{3}{*}{GEV} & \(\gamma\) & 0.496 \\  & \(\beta\) & 2.446 & & \(k\) & 0.902 \\ \hline \multirow{2}{*}{Weibull} & \(\alpha\) & 1.008 & \multirow{2}{*}{GEV} & \(\mu\) & 0.864 \\  & \(\beta\) & 2.693 & & \(\sigma\) & 0.963 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter estimation results of candidate models for temporary users. both larger than 0.001).