Ph.d.-forelæsning/PhD Defense, Heidi Søgaard Christensen

Title:
“Statistics for Point Processes on Linear Networks and on The Space Cross Sphere”

Abstract:
This thesis concerns point processes which are used for modelling a certain type of data, where each data point describes the location of an object or the time of an event. Such data are called point patterns and arise within a variety of applications as for example forestry, astronomy, neuroscience, criminology, or seismology, where the data points can describe the location of trees in a forest, the time and position of fireballs observed from Earth, the location of neurons in the brain, the site of crimes within a city, or the time of an earthquake. Thus point pattern data can be observed on a wide range of spaces such as one-, two-, and three-dimensional Euclidean spaces, spheres or linear networks. Depending on the nature of this space - and the way distance is measured - different tools and models exist for analyzing the point pattern. Most of the existing literature on point processes concerns Euclidean spaces, but some advances have also been made for point processes on linear networks or on spheres. In some cases, theory from the Euclidean space setup can easily be extended or modified to other types of spaces, but in other cases such extensions are not straightforward or even possible. The thesis concerns modelling and inference for point patterns on linear networks, the Euclidean space, or the product space between the Euclidean space and the sphere. Specifically two kind of point patterns are modelled in the thesis: one describing the orientation and location of pyramidal cells in a section of a human brain, and another describing the location of spines on a dendrite tree from a mouse neuron.