statistical methods for some emerging issues in modeling latent variables

拟议研究计划的目标是为涉及不可观测数量的复杂建模中出现的新问题开发统计方法。这些问题在许多研究领域(如健康科学、环境研究、计算机科学)中经常遇到，在这些领域中，数据生成系统是由不可观测的量驱动的。这项建议涵盖三大主题：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)为这些可能不容易计算似然函数的复杂模型设置开发模型估计的计算方法；(2)评估错误指定复杂模型系统的一部分(S)的后果；(3)开发为模型系统选择重要变量的统计方法；以及(4)构建检验假设模型的拟合优度的统计检验。

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.