  Bump hunting deals with finding in sample spaces meaningful data subsets
known as bumps. These have traditionally been conceived as modal or concave
regions in the graph of the underlying density function. We define an abstract
bump construct based on curvature functionals of the probability density. Then,
we explore several alternative characterizations involving derivatives up to
second order. In particular, a suitable implementation of Good and Gaskins'
original concave bumps is proposed in the multivariate case. Moreover, we bring
to exploratory data analysis concepts like the mean curvature and the Laplacian
that have produced good results in applied domains. Our methodology addresses
the approximation of the curvature functional with a plug-in kernel density
estimator. We provide theoretical results that assure the asymptotic
consistency of bump boundaries in the Hausdorff distance with affordable
convergence rates. We also present asymptotically valid and consistent
confidence regions bounding curvature bumps. The theory is illustrated through
several use cases in sports analytics with datasets from the NBA, MLB and NFL.
We conclude that the different curvature instances effectively combine to
generate insightful visualizations.
