We develop a Bayesian particle filter for tracking traffic flows that is capable of capturing non-linearities and discontinuities present in flow dynamics. Our model includes a hidden state variable that captures sudden regime shifts between traffic free flow, breakdown, and recovery. We develop an efficient particle learning algorithm for real time online inference of states and parameters. This requires a two-step approach, first resampling the current particles with a mixture predictive distribution and second propagation of states using the conditional posterior distribution. Particle learning of parameters follows from updating recursions for conditional sufficient statistics. To illustrate our methodology, we analyze the measurements of daily traffic flow from the Illinois Interstate I-55 highway system. We demonstrate how our filter can be used to infer the change of traffic flow regime on a highway road segment based on a measurement from freeway single-loop detectors. Finally, we conclude with directions for future research.

This work investigates the inter-relationships among stream water quality indicators, hydroclimatic variables (e.g., precipitation, river discharge), and land characteristics (e.g., soil type, land use), which is crucial to developing effective methods for water quality protection. The potential of using statistical tools, such as Principal Component (PC) and Granger causality analyses, for this purpose is assessed across 10 watersheds in the Eastern United States. The PC analysis shows consistency across the ten locations, with most of the variation explained by the first two PCs, except for the least developed watershed that presents three PCs. Results show that stronger Granger causality relationships and correlation coefficients are identified when considering a lag of one day, compared to longer lags. This is mainly due to the watersheds’ limited size and, thus, their fast hydrological response. The strongest Granger causalities are observed when water temperature and dissolved oxygen concentration are considered as the effect of the other variables, which corroborates the importance of these two water properties. This work also demonstrates how watershed size and land use can impact causalities between hydrometeorological variables and water quality, thus, highlighting how complex these relationships are even in a region characterized by overall similar climatology.

Deep Learning (DL) is combined with extreme value theory (EVT) to predict peak loads observed in energy grids. Forecasting energy loads and prices is challenging due to sharp peaks and troughs that arise due to supply and demand fluctuations from intraday system constraints. We propose a deep temporal extreme value model to capture these effects, which predicts the tail behavior of load spikes. Deep long‐short‐term memory architectures with rectified linear unit activation functions capture trends and temporal dependencies, while EVT captures highly volatile load spikes above a prespecified threshold. To illustrate our methodology, we develop forecasting models for hourly price and demand from the PJM interconnection. The goal is to show that DL‐EVT outperforms traditional methods, both in‐ and out‐of‐sample, by capturing the observed nonlinearities in prices and demand spikes. Finally, we conclude with directions for future research.