Statistics Seminar

Abstract: Reliable future climate projection requires statistically principled methods that combine observations with multi-model climate simulations to constrain uncertainty. Existing statistical approaches formalize this idea by linking simulated historical and future climate responses and conditioning future projections on observations, but inference is typically conducted marginally at individual locations and does not account for spatial dependence across climate fields. This site-wise treatment limits uncertainty calibration and prevents coherent joint inference for spatial projections. We propose a hierarchical emergent constraint framework for joint observation-constrained projection of high-dimensional spatial climate fields. The relationship between historical and future responses is modeled through a spatial scaling matrix estimated via regularized generalized least squares, with spatial coherence enforced by a tree-guided equi-sparsity penalty. To address the small-ensemble, large-dimension regime, we develop a spiked shrinkage covariance estimator that stabilizes inverse covariance estimation and enables calibrated uncertainty propagation. The proposed framework yields a joint predictive distribution for future climate fields to enable coherent uncertainty quantification across space, supports theoretical guarantees under high-dimensional asymptotics, and produces spatially coherent and well-calibrated constrained projections in simulations and a temperature projection application.