statistical methods for some emerging issues in modeling latent variables

拟议的研究计划的目标是开发统计方法，在复杂的建模，涉及不可观测的数量所产生的新问题。这些问题在许多研究领域（例如健康科学，环境研究，计算机科学）中经常遇到，其中数据生成系统由不可观测的量驱动。该提案涵盖了三个广泛的主题：变量误差模型，计数数据的时间序列模型和复杂数据的随机效应模型。这项工作的主要目标是：（1）开发用于这些复杂模型设置的模型估计的计算方法，其中可能不容易计算似然函数，（2）评估错误地指定复杂模型系统的部分的后果，（3）开发用于选择模型系统的重要变量的统计方法，以及（4）构造用于检查假设模型的拟合优度的统计检验。* 拟议工作的动机是真实的生活问题，研究成果将解决特定研究领域产生的问题（例如变量选择，模型检查）。 然而，要开发的方法将是广泛的，因此预计它们将在各种应用中使用。 * 最终，拟议的研究将丰富统计方法工具箱，并为统计以外的最终用户提供实用指南。 **

The objective of the proposed research program is to develop statistical methodologies for emerging issues arising in complex modeling that involve unobservable quantities. These issues are commonly encountered in many research areas (e.g. health science, environmental studies, computer science) in which the data generating system is driven by unobservable quantities. This proposal covers three broad topics: errors-in-variables models, time series models for count data, and random effects models for complex data. The main goals of the work are to: (1) develop computational methods for model estimation for these complex model settings where the likelihood function may not be easily computed, (2) assess the consequences of wrongly specifying part (s) of the complex model system, (3) develop statistical methods for selecting important variables for the model system, and (4) construct statistical tests for checking the goodness-of-fit of the assumed model. ***The proposed work is motivated by real life problems and the outcomes of the research will resolve concerns (e.g. variable selection, model checking) arising from specific research areas. However, the methodologies to be developed will be broad and thus their use in a wide variety of applications is expected. ***Ultimately, the proposed research will enrich the toolbox of statistical methodologies and also provide practical guidelines for end-users from communities outside statistics. **