Methods for predictive models with longitudinal data

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Accurate prediction of future outcomes is a common goal in many areas of science (e.g., climate, earthquake, hydrology, medical, etc.). The goal in my research program is to develop new methods for prediction problems where data that are collected over time, i.e., longitudinal data, are used to help predict future events. ******My research program specifically focuses on the prediction of short-term events (within weeks or even days), with an eye on applications where there is potential saving of forests, or property, or life, etc., and for which early and sufficiently accurate predictions are of importance. A key trade-off in predicting future events is to balance the accuracy that predictions can have if following time-varying information right to the point that the event is about to occur, as opposed to making an early prediction before it is too late (as the event is imminent). For example, if prevailing winds suggest there is a certain positive probability that a large forest fire may engulf a proximal town in a couple of days, at what point does a decision for an evacuation take place, especially when there is also a chance for predicting a false positive event. Similar decisions can be important in the context of other events, such as earthquakes, volcanoes, hurricanes, and heat waves. Here, we would like to develop a decision-making process that appropriately accommodates the trade-off between (a) early decisions that may prevent injury or save life but also may lead to a higher rate of false positives and (b) later decisions that are more accurate (i.e., fewer false positives) but may lead to greater loss of quality-of-life or actual life. We need to also consider possible false negative decisions, i.e., by deciding not to act due to, for example, assuming the probability of an event is sufficiently low, but thereafter the event actually occurs. We can consider this entire decision-making process in terms of cost, and we would obviously like to minimize this cost. Various assumptions need to be made, including on probabilities and costs of false positives and false negatives, respectively. Comprehensive simulation studies will be a key component of this work, and we will find and analyze relevant real data sources (e.g., daily temperature and rainfall datasets) as well. In both simulations and real datasets, we will evaluate the accuracy of our predictions, both in absence of consideration of cost and in presence of different assumptions about costs. ******As mentioned above, this research work has relevance across various disciplines, including in statistics, and potentially environmental, hydrological, biological, and atmospheric sciences, among others. The findings that my trainees and I will produce will be useful for researchers in Canada and beyond, due to the ever-increasing need to properly predict future events, and to place proper costs on making incorrect decisions.**