statistical methods for some emerging issues in modeling latent variables

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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.