Professor of Statistics
Professor of Political Science
Director, Applied Statistics Center
Past Research: Professor Gelman's past research has been in two major areas: (1) statistical theory, methods, and computation, and (2) applications in political science, public health, and policy. His statistical work has centered on Bayesian inference, multilevel models, and graphical methods. Some important recent papers in these areas include a Bayesian formulation of the analysis of variance, a multiple-imputation approach to checking the fit of models with missing or latent data, average predictive comparisons for nonlinear models, new measures of partial pooling and explained variance for multilevel models, a new family of prior distributions for hierarchical variance parameters, a Bayesian approach to exploratory data analysis and statistical graphics, and a method for software validation using posterior quantiles. Gelman's recent applied papers cover topics including the incumbency advantage in congressional elections, racial patterns in police stops, the death-penalty appeals process, decision making for reducing arsenic in drinking water in Bangladesh, and the structure of social networks. In addition to these and other research projects, Gelman just published a book (with Jennifer Hill) on regression and multilevel models, including dozens of examples from his applied research.
Present Research: Gelman's current research focuses on building and checking multilevel models in applications including time series of public opinions, laboratory measurements of allergens, income and voting in elections, political polarization, and psychometrics. Current methodological research projects include a unification of survey weighting and regression modeling, a general approach for displaying regression inferences, and methods for checking the fit and reasonableness of missing-data imputations. A key theme running through Gelman's recent applications is the importance of interaction effects; in an experimental or observational study, interactions correspond to treatment effects that are different for different groups of the population. Gelman has been developing multilevel models for such patterns that occur across a range of substantive applications, including voting, public health, and educational measurement.
Future Research: Gelman anticipates future work that continues developing methods for more complex multilevel models. The complexity is necessary for more realistic models of social and environmental patterns. Along with these more advanced models must come general methods for understanding and evaluating goodness-of-fit. Gelman will be pursuing research on model-building tools that go beyond residual plots and tables of coefficients to integrate exploratory data analysis with complex modeling. Also, Gelman is conducting research on efficient computational methods, including threaded looping to implement Bayesian inference for sequential multiple imputations and redundant parameterization for hierarchical models. Gelman's future work will apply these methods to various ongoing and new projects, including a current NSF-funded study of social and political polarization using survey data and a current NIH-funded program for analysis of laboratory assays. Gelman directs the Applied Statistics Center, which has connections with over a dozen departments, schools, and institutes at Columbia, and he is also conducting an ongoing series of methodological workshops with faculty at the Columbia School of Social Work.
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