New methods for predictive models for univariate and multivariate longitudinal response data

对未来结果的准确预测是许多科学领域（如气候、生物、医学等）的共同目标。我的研究计划的目标是开发新的方法来预测不仅仅是二元事件，而是纵向结果的轨迹，包括有多个这样的结果的问题（即，多变量纵向响应）。这些努力将用于包含单变量或多变量纵向响应的问题，这些响应可以稀疏地或集中地收集，并且在多变量情况下，可能是异步的。我们的第一个目标是为单变量纵向反应开发灵活的预测模型，其中评估的基础是提高在个体水平上预测单一反应轨迹的准确性。这是一个使用动态建模进行研究的领域，随着时间的推移收集到更多的数据，轨迹预测也会更新。然而，对于某些问题，早期预测是必要的（并且不能等待继续动态更新预测）；我们将在这里重点讨论这个设置。这些场景的例子包括潜在的紧急情况，如河流可能发生洪水或即将到来的热浪。为了帮助改进这些对纵向轨迹的早期预测，我建议将相似性的概念纳入其中。这种方法利用以前情景的特征（例如，过去类似气候的温度轨迹）来帮助了解在给定的新环境中可能发生的情况，而不是考虑所有可能的历史情景；从本质上讲，使用战略选择的前场景的子集，并且需要就如何识别和适当地权衡类似场景来提高预测准确性做出决策。这个目标的一部分将继续在预测多变量纵向响应轨迹的更复杂的问题中研究相似方法。对于第二个目标，将考虑一个完全不同的环境来预测假定由潜在过程驱动的多变量纵向响应轨迹，其中我们将开发一种隐马尔可夫建模（HMM）方法；这项工作将建立在之前的工作基础上，之前的工作是用混合HMM建模多变量纵向数据。为了实现这两个目标，我们将在贝叶斯范式下进行操作，该范式允许通过预测密度直接进行统计推断，同时克服一些困难的计算挑战，特别是对于混合HMM方法。该研究项目在预测建模方面做出了新的贡献，这些贡献与各个学科相关，包括统计学和其他科学领域（如气候、生物学），并可应用于一些实际的紧急情况。因此，我和我的学员将产生的方法应该对加拿大和其他国家的研究人员有价值。

Accurate prediction of future outcomes is a common goal in many areas of science (e.g., climate, biology, medical, etc.). The goal in my research program is to develop new methods for predicting not simply binary events but instead trajectories of longitudinal outcomes, including for problems where there is more than one such outcome (i.e., multivariate longitudinal responses). These efforts will be for problems containing univariate or multivariate longitudinal responses which may be collected either sparsely or intensively, and, in the multivariate case, possibly asynchronously. Our 1st objective is to develop flexible predictive models for univariate longitudinal responses, where the basis of evaluation is improving the accuracy of predicting single response trajectories at the individual level. This is an area that has been studied using dynamical modeling, where the trajectory predictions are updated as more data over time are collected. However, there are problems for which early predictions are necessary (and there is not the luxury of waiting to continue to update predictions dynamically); we will focus on this setting here. Examples of such scenarios include potential urgent situations, such as a river possibly flooding or a heat wave impending. To help improve these early predictions of longitudinal trajectories, I propose incorporating the concept of similarity. This approach uses characteristics of former scenarios (e.g., temperature trajectories in similar climates in the past) to help inform what might happen in a given new setting, instead of considering all possible historical scenarios; essentially, a subset of strategically chosen former scenarios is used, and decisions need to be made on how to both identify and weight suitably similar scenarios to improve predictive accuracy. Part of this objective will continue with the similarity approach investigated in the more complex problem of predicting multivariate longitudinal response trajectories. For the 2nd objective, an entirely distinct context for predicting multivariate longitudinal response trajectories that are assumed driven by latent process(es) will be considered, where we will develop a hidden Markov modeling (HMM) approach; this work will build from previous work with a former trainee in modeling multivariate longitudinal data with mixed HMM's. To accomplish both objectives, we will operate under the Bayesian paradigm, which allows for a direct approach to statistical inference via predictive densities, while overcoming some difficult computational challenges, particularly for the mixed HMM approach. This research program comprises novel contributions in predictive modeling that are relevant to various disciplines, including in statistics and other areas of science (e.g., climate, biology) and could be applied in some practical urgent settings. Hence, the methods that my trainees and I will produce should be valuable for researchers in Canada and beyond.