## 2 Contemporary Model- and Data Driven (Crowd) Forecasting Methods
### Data-Driven Forecasting of Traffic  
In other transport-related fields, more specifically the modelling of highway and urban vehicular traffic, several interesting techniques have been introduced that can possibly be adapted to forecast crowd movements. These data-driven traffic forecasting techniques can be subdivided in three categories, being: (1) filtering techniques and stochastic models that use very limited historic information when trained, (2) time series models and machine learning algorithms that incorporate some information regarding the transition probability between states and (3) machine learning algorithms that incorporate information about the recent past of the system in real-time when computing the future state of the system. The first group is dominated by Kalman Filter and Particle Filter applications. The Kalman Filtering technique, developed by [35], is a unified approach for the prediction of processes with a state-space representation (e.g., [36; 37]). Most applications of the Kalman Filter (KF) improve the filter by adding additional knowledge regarding the forecasting problem, for example traffic engineering principles. The generic version of the Kalman Filter is a linear approximation. The Extended Kalman Filter (EKF), which is an extension of the Kalman Filter, is better equipped to also capture non-linear trends in traffic data (e.g., [38]). The Particle Filter (PF), applied among others by [39; 40], computes the posterior distribution of the states given noisy and partial observations. KFs, EKFs and PFs have a low data requirement, limited model description and low computational effort. Next to that, these filters react to local data, and can as such be categorized as techniques that incorporate very little memory regarding previous traffic states. Over the years, several uni- and multivariate time series models and simple neural networks have been introduced for traffic forecasting purposes, many of which incorporate the average dynamics of historic data. Most used are Gaussian Maximum Likelihood models (GML), support vector machines (SVM/SVR) and Hidden Markov Models (HMM). GML models forecast traffic using a stochastic model that combines the statistical properties of historic traffic data with real-time traffic data (e.g., [41]). This model type is simple to implement, robust and especially good at predicting global trends in traffic data, such as traffic flows. SVR is a universal learning method developed by [42]. Using the statistical properties of traffic, such as the day-to-day and within-day variation, and observational data, a statistical model is estimated. This model is accordingly used to, among other things, predict traffic volumes. Traditional SVR, introduced by [41], requires complete model training whenever new data point is added, while the online SVR (OL-SVR) can react to the current state of traffic without fully retraining the model [43; 44]. HMMs forecast traffic by means of a set of pre-defined states and state transition probabilities between states. A HMM estimates the most likely sequence of traffic states [45]. This type of model assumes that the future state is independent of past realisations. As a result thereof, this model is officially memory-less. Yet, as the state transition probabilities are trained using historical traffic data, the model'remembers' the average dynamics captured within the historical data. Shallow neural networks (NN) have proven to be a powerful modelling technique, which forecasts traffic using a net of interconnected linear processing elements. Neural networks are non-parametric; therefore no assumptions regarding the functional form of the underlying distribution of the data need to be made [46]. This technique can capture non-linear dependencies, but only incorporate memory regarding the average state of a traffic system. The last group of traffic forecasting techniques features machine learning.