Probability metrics and metrics between spatial point patterns
Study of probability metrics from a general point of view, with main emphasis on Wasserstein metrics. Based on the Wasserstein / optimal transport idea, construction of various metrics between point patterns and theoretical study of them and of the associated probability metrics between point process distributions.
Stein's method for distributional approximation
Investigation of Stein's method for point process approximation (Poisson, Gibbs, ...) in the above probability metrics and derivation of explicit rates for point process limit theorems.
Methodology for spatial point pattern analysis
Various methods for spatial point pattern analysis. Approximation of correlation functions / densities of moment measures.
Density estimation under qualitative constraints
Theoretical properties of estimators based on nonparametric maximum likelihood estimation of a probability density under a log-concavity assumption. Recent projects include regression models with log-concave error distribution and estimation of a log-concave density based on interval-censored data.
Development of algorithms and their implementation in various R functions and packages, including the function pppdist in spatstat for computing distances between spatial point patterns.