Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.

A Longitudinal Investigation of Infant Gesture Use and Parent Speech: Unique and Dynamic Influences on Infant Vocabulary Acquisition

How do infants learn word meanings? Research has established the impact of both parent and child behaviors on vocabulary development, however the processes and mechanisms underlying these relationships are still not fully understood. Much existing literature focuses on direct paths to word learning, demonstrating that parent speech and child gesture use are powerful predictors of later vocabulary. However, an additional body of research indicates that these relationships don’t always replicate, particularly when assessed in different populations, contexts, or developmental periods.

The current study examines the relationships between infant gesture, parent speech, and infant vocabulary over the course of the second year (10-22 months of age). Through the use of detailed coding of dyadic mother-child play interactions and a combination of quantitative and qualitative data analytic methods, the process of communicative development was explored. Findings reveal non-linear patterns of growth in both parent speech content and child gesture use. Analyses of contingency in dyadic interactions reveal that children are active contributors to communicative engagement through their use of gestures, shaping the type of input they receive from parents, which in turn influences child vocabulary acquisition. Recommendations for future studies and the use of nuanced methodologies to assess changes in the dynamic system of dyadic communication are discussed.