# Probabilistic Forecasting of Electricity Demand Incorporating Mobility Data
## 4 Discussion and Conclusions  
EDF is critical in the energy sector, and uncertainties that affect energy demand predictions must be considered. Conventional point EDF cannot precisely capture this uncertainty. This paper utilizes GPR, which can deal with anomalous events with minimal data. GPR has recently acquired attention in the literature as a non-parametric probabilistic forecasting method. Most articles incorrectly assumed the GPR approach was deterministic and failed to fully use its benefits. To bridge this gap, this research aimed to model EDF as a regression issue and developed a comprehensive short-term probabilistic EDF based on GPR-KDE methods to depict unprecedented events. This study also proposed using mobility data to include social and economic behaviors in forecasting algorithms to demonstrate the human behavior pattern (practice theory [46]) as further characteristics to deal with the uncertainty caused by anomalous events such as floods, bushfires, and pandemics. Therefore, firstly, a correlation study is carried out to identify the features highly related to electricity demand. Four factors were identified as significantly impacting the EDF: temperature, renewable and non-renewable energy sources, and human mobility (specifically workplace and res  
Figure 8: Test error plot for GPR (Exponential kernel) model of three scenarios. idential) data. After identifying the highly correlated features, three widely-used kernel functions were examined to find the optimal one for modelling complex interactions. It identified the Exponential covariance function as a great kernel function. Finally, GPR is applied for EDF and compared with different models and kernel functions to provide point forecasting along with comprehensive probability estimation for prediction intervals. Then, the model forecasting results under different CI are input into the KDE function to estimate the probability distribution. Several testing and validation techniques were used to examine the performance of the proposed method for predicting EDF using real data; 5-fold cross-validation was used for model validation in addition to the other statistical technique. Results showed that the Exponential covariance function performed well among other kernels used in this study to evaluate the EDF. In addition, it is crucial to compare with other recent studies to further demonstrate the efficacy of the proposed method. It is imperative to utilize the same data set to make the comparison significant. However, to the best of our knowledge, no study in the literature has investigated the EDF using a similar data set and timeframe. Therefore, this study demonstrated the proposed method's implementation in three different scenarios in Australia to establish the model's accuracy. The results show:  
* GPR has been averagely improved compared to BPNN, RT, and SVR in the case of point forecasting by 59%, 79%, and 51%, respectively. * The system was validated for one-day-ahead weather forecasts and the most typical time horizon using the PICP and MPIW indicators. The PI results of three scenarios with different confidence levels (95%, 90%, 80%, and 50%) indicate that most of the real electricity demand falls into the PIs with 50-80% CI, which demonstrates the accuracy of the proposed method. Under the same PICP condition, the MPIW of the proposed method GPR (exponential kernel) is much smaller than that of other compared kernels. * Meanwhile, a large number of real electricity demand values are located near the peak of probability density curves. The CRPS for the probabilistic forecast is better than the MAE value of the point forecasting. This study's results show that GPR-KDE is a reliable method and can still produce a very accurate forecast of complex electricity demand patterns with limited historical data. Different restriction measures in both scenarios 2 and 3 during the pandemic and their impact on people's activities have considerably changed the electricity demand profile distinctively.