Methods for predictive models with longitudinal data

准确预测未来结果是许多科学领域的共同目标（例如，气候、地震、水文、医疗等）。在我的研究计划的目标是开发新的方法来预测的问题，随着时间的推移收集的数据，即，纵向数据被用来帮助预测未来的事件。** 我的研究项目特别关注短期事件（数周甚至数天内）的预测，着眼于有可能拯救森林，财产或生命等的应用。并且早期和足够准确的预测对于这些是重要的。预测未来事件的一个关键权衡是平衡预测的准确性，如果跟随时变信息直到事件即将发生，而不是在为时已晚之前做出早期预测（因为事件即将发生）。例如，如果盛行风表明有一定的正概率，一场大的森林大火可能在几天内吞没附近的城镇，那么在什么时候做出疏散的决定，特别是当也有可能预测一个假阳性事件时。类似的决定在其他事件的背景下也很重要，比如地震、火山、飓风和热浪。在这里，我们希望开发一种决策过程，该决策过程适当地适应（a）可以防止伤害或挽救生命但也可能导致更高的误报率的早期决策与（B）更准确（即，更少的假阳性），但可能导致生活质量或实际生活的更大损失。我们还需要考虑可能的假阴性决定，即，通过例如由于假设事件的概率足够低而决定不采取行动，但是此后事件实际发生。我们可以从成本的角度来考虑整个决策过程，我们显然希望将成本降至最低。需要作出各种假设，包括分别对误报和漏报的概率和代价作出假设。全面的模拟研究将是这项工作的关键组成部分，我们将找到并分析相关的真实的数据源（例如，每日温度和降雨量数据集）。在模拟和真实的数据集中，我们将评估我们预测的准确性，无论是在不考虑成本的情况下，还是在存在不同的成本假设的情况下。* 如上所述，这项研究工作涉及各个学科，包括统计学，以及潜在的环境，水文，生物和大气科学等。我的学员和我将产生的研究结果将对加拿大和其他地区的研究人员有用，因为人们越来越需要正确预测未来事件，并为做出不正确的决定付出适当的代价。

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.**