Publications

Shape-constrained density estimation poses a middle ground between fully nonparametric and fully parametric density estimation. Log-concavity is a common choice of shape constraint. Using universal inference, we develop the first test for log-concavity that is provably valid. Validity holds in finite samples.

We extend conformal prediction methods to a two-layer hierarchical setting. Conformal prediction constructs valid prediction sets in finite samples, even if the predictive model is incorrect.

The universal LRT provides finite-sample valid hypothesis tests and confidence sets in any setting for which we can compute the likelihood ratio. We present the first in-depth exploration of the size, power, and relationships between several universal LRT variants. We illustrate the benefits of the universal LRT in a test of a non-convex doughnut-shaped null hypothesis.

We construct the first risk score for end-stage knee OA, using an end-stage definition that depends on symptomatic and radiographic criteria. We note particular implications for clinical trial patient selection.

We construct prediction bands for tropical cyclone paths. We also develop a publicly available computational pipeline for this task.