Dynamic Objects on Random Fields

• Applicant: Professor Dr. Johannes Theodor Nikolaus Krebs
• Subject Area: Mathematics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 375055887

The research fellowship prepares me for my further scientific career in Germany, in particular for the application for an assistant professor position. I have been a doctoral student of Prof. Dr. Jürgen Franke at the chair of Statistics at the University of Kaiserslautern since July 2014. The topic of my dissertation is Sieve Estimators for Spatial Data – Nonparametric Regression and Density Models with Wavelets for Strong Mixing Random Fields. The defense of the doctoral thesis is expected to take place between January and March 2017. My further academic background is the following: I studied economics at the University of Mannheim from 2006 to 2009 and graduated with a Bachelor’s degree. Furthermore, I studied mathematics at the University of Kaiserslautern from 2009 to 2013 and graduated with a Bachelor’s and a Master’s degree. Now I want to deepen my knowledge in mathematics and statistics abroad and simultaneously strengthen my scientific network.The project is in parts a continuation of my dissertation. In this way, I can well use my acquired skills. The project aims at extending the established methods in the statistical modelling of high- and infinite-dimensional data to random fields. A random field is a stochastic process which is defined on a spatial index set, e.g., longitude and latitude. So far these models have mostly been used for independent data or time series. The statistical investigation in the spatial context is new. It greatly generalizes this theory, here the dependence structures are much more complex.The project allows us to explain spatial phenomena in a mathematical way: in many research questions high-dimensional or even continuously measured data are collected on a spatial network. In this context a network is defined as a graph with nodes and edges. The data often causally interact with each other or are at least strong (stochastically) dependent. Notable examples are phenomena in traffic networks as the traffic density. Here there is an obvious causal relationship between the observations on the single nodes. Further examples are climatologic events such as temperature and precipitation distributions across a country. Firstly, the new developed methods enable us to study inheritance patterns for the collected data. This means, we can make quantitative statements on how exactly observations in a network depend on the observations in their neighborhood and whether there is a causal relationship which can be expressed by a function. Secondly, we can identify structural breaks within networks. This means that we use statistical tests to determine regions within the network that significantly differ from each other.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. Wolfgang Polonik