Applied Probability and Statistics

Applied Probability and Statistics

The following research topics within applied probability and statistics are of particular interest at the department.

Biodiversity: The high tree species diversity of tropical rain forests is of key interest in ecological research where one aim is to infer mechanisms contributing to biodiversity from the spatial pattern of trees. A challenge in this respect is that the effects of diffent mechanisms are entangled. Indeed, con-specific aggregation in the pattern of trees may e.g. result both from adaptation of a species to a certain environment and from seed dispersal limitation where offspring are generated in the vicinity of parent trees. Statistical methodology for inhomogeneous spatial point processes (with several key contributions from the spatial statistics group) offers a natural and useful approach to disentangle the effects of the various mechanisms.

Bioimaging: Förster resonance energy transfer (FRET) microscopy is an imaging technique which allows for indirect measurements of proximity of proteins at the nano scale, where conventional microscopy cannot be used. The indirect measure of proximity is a non-linear function of three different color intensities, and Ege Rubak, Jan-Otto Hooghoudt and Rasmus Waagepetersen develop statistical tools for analyzing these types of data. In particular there is a great interest in evaluating any departure from complete spatial randomness in the arrangement of proteins.

Micro-columns: a debated hypothesis in neuro-science is that neurons and glia cells in the cerebral cortex (outer layer of the brain) form column-like structures which may be associated with various diseases such as schizophrenia. Farzaneh Safavimanesh, Jesper Møller and Jakob Gulddahl Rasmussen develop methodology based on theory for three-dimensional spatial point processes with the aim of investigating the micro-column hypothesis.

Stochastic geometry deals with models for random sets, and two major topics are spatial point processes and random tessellations. Jesper Møller has particularly focused on developing a fundamental theory for random Voronoi and Johnson-Mehl tessellations, the two most important model classes of random tessellations. He has also studied the probabilistic aspects of various model classes for spatial point processes with applications in e.g. computer science. Jakob G. Rasmussen has studied various properties of Hawkes processes, an important class of point processes used e.g. in seismology, where he has focused on simulation of and inference for such processes.

Baggage handling: lost luggage in the aviation industry due to mishandling is a well-known problem. The purpose of the BagTrack project is to build a system which can evaluate the quality of the bag handling process based on data collected from so-called RFID tags attached selected bags. Shima Shahbazi and Kasper Berthelsen develop statistical tools for selecting bags for tagging, assessment of handling quality based on tag data, and for analysis of the handling processes.

Other topics: Econometrics, Spatial and Computational Statistics, Statistical Genetics and Bioinformatics.