statistical methods for some emerging issues in modeling latent variables

提出的研究计划的目标是为涉及不可观测量的复杂建模中出现的新问题开发统计方法。这些问题通常在许多研究领域（例如健康科学、环境研究、计算机科学）中遇到，其中数据生成系统是由不可观察的数量驱动的。该建议涵盖三个广泛的主题：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)为这些复杂的模型设置开发模型估计的计算方法，其中似然函数可能不容易计算；(2)评估错误指定复杂模型系统部分的后果；(3)开发为模型系统选择重要变量的统计方法；(4)构建用于检查假设模型的拟合优度的统计检验。***建议的工作是由现实生活中的问题和研究的结果将解决问题（如变量选择，模型检查）产生的具体研究领域。但是，将要开发的方法将是广泛的，因此预期它们将用于各种各样的应用。***最终，拟议的研究将丰富统计方法的工具箱，并为统计以外社区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. **