Methods for predictive models with longitudinal data

对未来结果的准确预测是许多科学领域(如气候、地震、水文学、医学等)的共同目标。我的研究计划的目标是为预测问题开发新的方法，其中随着时间的推移收集的数据，即纵向数据，用于帮助预测未来的事件。*我的研究计划特别关注短期事件的预测(在几周甚至几天内)，着眼于那些有可能拯救森林、财产或生命等的应用，对这些应用来说，早期和足够准确的预测是重要的。预测未来事件的一个关键权衡是平衡预测可能具有的准确性，如果跟踪时变信息准确到事件即将发生，而不是在为时已晚(事件迫在眉睫)之前做出早期预测。例如，如果盛行的风向表明，一场森林大火可能会在几天内吞没附近的城镇，那么在什么时候会做出疏散决定，特别是在也有可能预测到假阳性事件的情况下。在地震、火山、飓风和热浪等其他事件的背景下，类似的决定可能很重要。在这里，我们希望制定一种决策过程，适当地权衡以下两者之间的权衡：(A)可能防止受伤或挽救生命但也可能导致较高假阳性率的早期决定，以及(B)更准确(即较少的假阳性)但可能导致更大的生活质量或实际生活损失的后来决定。我们还需要考虑可能的错误否定决定，例如，由于假设事件的概率足够低而决定不采取行动，但此后事件实际上发生了。我们可以从成本的角度来考虑整个决策过程，我们显然希望将这一成本降至最低。需要做出各种假设，包括分别关于假阳性和假阴性的概率和成本。全面的模拟研究将是这项工作的关键组成部分，我们还将找到并分析相关的真实数据来源(例如，每日温度和降雨量数据集)。在模拟和真实数据集中，我们将评估我们预测的准确性，无论是在没有考虑成本的情况下，还是在存在关于成本的不同假设的情况下。*如上所述，这项研究工作涉及多个学科，包括统计学、环境科学、水文学、生物科学和大气科学等。我和我的学员将得出的结果将对加拿大国内外的研究人员有用，因为人们越来越需要正确预测未来的事件，并为做出错误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.**