Overview
Andrew Gelman is a statistician at Columbia University (Department of Statistics and Department of Political Science). His research spans Bayesian inference, hierarchical modeling, model checking, causal inference, and applied statistics. He is the lead author of Bayesian Data Analysis (with Carlin, Stern, and Rubin), the standard graduate text in the field.
Key Contributions
- Gelman-Meng-Stern (1996): Developed the posterior predictive check framework using realized discrepancies D(y;θ) and the posterior predictive p-value pb(y). Introduced the three-replication-type taxonomy (posterior/prior/mixed predictive). See Posterior Predictive Check.
- Gelman-Rubin (1992): Proposed the R^ convergence diagnostic for MCMC using multiple parallel chains; still the standard diagnostic in practice.
- Bayesian Data Analysis (with Carlin, Stern, Rubin, 1995): Foundational graduate textbook covering Bayesian modeling, computation, and model checking.
- Gelman-Pardoe (2004): Proposed level-specific R² (proportion of level-m variance explained by predictor μ, eq. 7) and pooling factor λ (fraction of residual variance reduced by hierarchical shrinkage, eq. 8); derived Bayesian adjusted R² with (n−3)/(n−p−2) correction; applied to Minnesota radon data (919 houses, 85 counties): uranium explains 83% of county-slope variation (R²_β=0.83), pooling factor λ_β=0.97; λ specializes to Bühlmann credibility weight ω for balanced one-way models. See Bayesian Hierarchical Model.
- Gelman-Shor-Bafumi-Park (2007): Resolved the rich-state/poor-state voting paradox — rich individuals vote Republican, rich states vote Democratic — using a varying-intercept, varying-slope multilevel logistic regression Pr(yi=1)=logit−1(αs[i]+βs[i]xi) with state-level regressions αs=aα+bαus+εsα, βs=aβ+bβus+εsβ; key finding b^β<0 — income slope steepest in poor states (Mississippi), near-zero in rich states (Connecticut); pattern emerged post-1992; county-level model and race controls confirm results. See Bayesian Hierarchical Model.
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