# A Comparative Study on Traffic Modeling Techniques for Predicting and Simulating Traffic Behavior
## 4 Spatiotemporal Traffic Prediction Models
### Summary of Spatiotemporal Traffic Prediction Models

Table 1: Comparison between ST-Kriging, Bayesian inference, and ANNs. traffic data that are large in size. In contrast, large traffic data produce samples that help to improve the prediction accuracy [47]. From the perspective of evaluating the model performance, ST-Kriging methods can be evaluated using cross-validation techniques and fundamental statistical parameters such as the variance of errors. Additionally, examining the model residuals helps assess the minimum variance of linear unbiased predictors [48]. Turning now to the data structure, ST-Kriging methods were implemented to model data with a Gaussian distribution. ST-Kriging does not perform the best when the value we want to predict indicates that there is a non-normal distribution, where the values either are higher or lower than the real values [49]. [PERSON] et al. [41] showed that probabilistic inference by using Bayesian belief networks is NP-hard. As a result, it is unlikely that a generalized algorithm will be designed in order to perform probabilistic inference efficiently in Bayesian belief networks over all possible classes. Therefore, for each of the special case, average case, and approximation algorithms, specific domain-centric Bayesian inference needs to be applied. In Bayesian inferences, the prediction accuracy depends on reducing the uncertainty of the posterior distribution, where the Bayesian inference generates samples \(\theta_{1},\theta_{2},\ldots,\theta_{n}\) from the posterior distribution. These generated samples will be updated using the Markov chain Monte Carlo (MCMC) algorithm until reaching the accurate posterior predictive distribution, which can be represented by the maximum likelihood [46]. Informative priors increase the accuracy of the Bayesian inference since they provide prior knowledge to help build the likelihood function. However, using informative priors requires more data to update the posterior since the posterior will be very much driven by the prior information. Computing more data can dominate the posterior distribution and cause an overfitting problem. The computational complexity in a Bayesian inference manifests in the MCMC algorithm's intensive computation required to compute the maximum likelihood estimation. Furthermore, when modeling traffic data that have a short temporal component using Bayesian inference, the MCMC algorithm's computational cost increases dramatically due to the high dimension of the temporal component [47]. In addition, improper priors can maximize the variance in the posterior samples, and hence more computational time is needed to identify the proper prior in order to reduce the variance in each sample [50]. Overall, estimating priors is a computationally intensive process, and this is considered one of the drawbacks of the Bayesian inference approach. Despite this, Bayesian inference has the capability to handle large traffic data with missing values and assign priors to these missing values [48]. It can also model data that are small in size, such as one observation, and be able to compute the prior of one observation. This process can be performed iteratively in real time [49]. Another advantage of Bayesian inference is that it can handle multilevel models and compute its hyperparameters [34]. In terms of evaluating the model performance, it is recommended to use coefficient estimates and standard deviation errors to measure the uncertainty of the model performance. When comparing the neural network approach to the previous approaches, specifying the proper network structure can affect the prediction accuracy, while optimizing the network structure can be achieved through experience [40]. Moreover, training ANNs can lead to an overfitting problem. Therefore, it is important to ensure that the validation accuracy is higher than the training accuracy [51]. Various ANN architectures, such as the multilayer perceptron (MLP) and fuzzy neural network (FNN), can be combined to predict the values of MPEG and JPEG video, Ethernet, and Internet traffic data one step ahead.