We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f which is close to, but simpler than, f . The surrogate captures the significant features in f . We establish lower bounds on the width for any confidence band for f and construct a procedure tha...

We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article contributes conceptual work on locally adaptive inference as a straightforward modification of the global setting imposes severe obstacles for statistical purposes....

The chemical bond arises from a redistribution of electronic charge when atoms are brought in close proximity. The bond in a solid results from the superposition of charge densities of all atoms in the system. In an atom all electrons reside in their ground states at equilibrium. Only a few low lying excited states are typically accessed. The chemical bond in the solid consists of excited elect...

Locust swarms cause famine and hunger in parts of Sub-Saharan Africa as they travel across croplands and eat vegetation. Current models start with biological properties of locusts and analyze the macroscopic behavior of the system. These models exhibit the desired migratory behavior, but do so with too many parameters. To account for this, a new model, the Alignment and Intermittent Motion (AIM...