New methods for predictive models for univariate and multivariate longitudinal response 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、生物学、医学等）。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，包括有不止一个这样的结果的问题（即，多变量纵向响应）。这些努力将包含单变量或多变量的纵向响应，可以收集稀疏或密集的问题，并在多变量的情况下，可能异步。我们的第一个目标是为单变量纵向响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响应轨迹的准确性。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数据，轨迹预测会更新。然而，对于某些问题，早期预测是必要的（并且没有等待继续动态更新预测的奢侈）;我们将在这里关注此设置。这种情况的例子包括潜在的紧急情况，如河流可能洪水或热浪即将到来。为了帮助改善这些早期预测的纵向轨迹，我建议纳入相似性的概念。这种方法使用以前场景的特征（例如，过去类似气候中的温度轨迹），以帮助告知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;基本上，使用了战略选择的先前情景的子集，并且需要就如何识别和适当加权类似情景以提高预测准确性做出决定。这一目标的一部分将继续与相似性的方法，在更复杂的问题预测多变量纵向响应轨迹。对于第二个目标，一个完全不同的背景下预测多变量纵向响应轨迹，假设驱动的潜在过程（ES）将被考虑，在那里我们将开发一个隐马尔可夫模型（HMM）的方法;这项工作将建立从以前的工作与前学员在建模多变量纵向数据与混合HMM的。为了实现这两个目标，我们将在贝叶斯范式下操作，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。该研究计划包括与各个学科相关的预测建模方面的新贡献，包括统计学和其他科学领域（例如，气候，生物学），并可以应用于一些实际的紧急情况。因此，我的学员和我将产生的方法应该是有价值的研究人员在加拿大和超越。

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.