Department of Statistics, UCLA

Recent advances in causal inference have given rise to a general and easy-to-use estimator for assessing the extent to which the effect of one variable on another is mdiated by a third. This estimator, called Mediation Formula, is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of path-specific effects with minimal assumptions regarding the data-generating process. We demonstrate the use of the Mediation Formula in simple examples and illustrate why parametric methods of analysis yield distorted results, even when parameters are known precisely. We stress the importance of distinguishing between the necessary and sufficient interpretations of “mediated-effect” and show how to estimate the two components in nonlinear systems with continuous and categorical variables.

WHAT PROBLEM DO WE ASPIRE TO SOLVE? We want to walk away from the traditional overview of statistics as a discipline that reliesupon repetitive procedures with fictitious datasets and major emphasis on step-wise and structured procedures.

INSTEADWe want to present applied statistics as aninterdisciplinary approach that allows thestudents to use statistics to answer real world questions and communicate statistical results.

HOW ARE WE APPROCAHING THIS DILEMMA?Implementation of case-based approach along with "generative model of teaching" and "technical writing"

With the growing capabilities of Geographic Information Systems(GIS) and user-friendly software, statisticians today routinely encounter geographicallyreferenced data containing observations from a large number of spatial locationsand time points. Over the last decade, hierarchical spatiotemporal processmodels have become widely deployed statistical tools for researchers to better understandthe complex nature of spatial and temporal variability. However, fittinghierarchical spatiotemporal models often involves expensive matrix computationswith complexity increasing in cubic order for the number of spatial locations andtemporal points. This renders such models unfeasible for large data sets. Thisarticle offers a focused review of two methods for constructing well-defined highlyscalable spatiotemporal stochastic processes. Both these processes can be used as“priors” for spatiotemporal random fields. The first approach constructs a lowrankprocess operating on a lower-dimensional subspace. The second approachconstructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparseprecision matrices for its finite realizations. Both processes can be exploited asa scalable prior embedded within a rich hierarchical modeling framework to deliverfull Bayesian inference. These approaches can be described as model-basedsolutions for big spatiotemporal datasets. The models ensure that the algorithmiccomplexity has ∼ n floating point operations (flops), where n the number of spatiallocations (per iteration). We compare these methods and provide some insightinto their methodological underpinnings.