doc. RNDr. Kateřina Helisová, Ph.D.

The thesis will describe mathematically exact definitions of outlying observations which often appear in mathematical statistics. Preliminary results show (see https://arxiv.org/abs/1507.07735) that these definitions are related to the theory of random sets, namely to the volume of the convex hull of multidimensional observations. The student will study the relationship between random sets and the classical distribution characteristics used in statistics, especially the issue of robust estimation of parameters of distribution families.

The research is focused on the field of stochastic geometry and spatial statistics, namely on statistical inference of inhomogeneous random sets. The aim is to develop new statistical methods which enable more accurate analysis than the methods currently available in spatial statistics. These are mainly non-parametric inferences and Bayesian parametric inferences based on the Markov Chain Monte Carlo approach.

The main task of PhD student is to develop new methods and to improve the existing procedures for modelling and statistical analysis of random geometrical objects, mainly the random closed sets. The work follows the research presented in supervisor's publications, which can be found on her web side.