Dynamic Objects on Random Fields

研究奖学金为我在德国进一步的科学生涯做好了准备，特别是申请助理教授职位。自2014年7月以来，我一直是凯撒大帝大学统计学系教授Jürgen Franke博士的博士生。我的学位论文题目是空间数据的筛估计-强混合随机场的非参数回归和小波密度模型。博士论文的答辩预计将于2017年1月至3月进行。我进一步的学术背景如下：2006年至2009年，我在曼海姆大学学习经济学，并获得学士学位。此外，我从2009年到2013年在凯撒大帝大学学习数学，并获得了学士学位和硕士学位。现在我想在国外加深我在数学和统计方面的知识，同时加强我的科学网络。这样，我就能很好地运用我学到的技能。该项目旨在将高维和无限维数据统计建模的既定方法扩展到随机领域。随机场是在空间索引集上定义的随机过程，例如，经度和纬度到目前为止，这些模型主要用于独立数据或时间序列。空间背景下的统计调查是新的。它极大地推广了这一理论，这里的依赖结构要复杂得多。该项目允许我们以数学的方式解释空间现象：在许多研究问题中，高维甚至连续测量的数据都是在空间网络上收集的。在这种情况下，网络被定义为具有节点和边的图。这些数据经常相互因果作用，或者至少是强（随机）依赖的。值得注意的例子是交通网络中的现象，如交通密度。在这里，单个节点上的观测之间存在明显的因果关系。进一步的例子是气候事件，如一个国家的温度和降水分布。首先，新开发的方法使我们能够研究所收集的数据的继承模式。这意味着，我们可以对网络中的观测值如何精确地依赖于其邻域中的观测值以及是否存在可以用函数表示的因果关系做出定量陈述。其次，我们可以识别网络中的结构断裂。这意味着我们使用统计测试来确定网络中彼此显著不同的区域。

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.