Estimation of Parameters in a Planar Segment Process With a Biological Application

Abstract

The paper deals with modeling of segment systems in a bounded planar set (a cell) by means of random segment processes. Two models with a density with respect to the Poisson process are presented. In model I interactions are given by the number of intersections, model II includes the length distribution and takes into account distances from the centre of the cell. The estimation of parameters of the models is suggested based on Takacz-Fiksel method. The method is tested first using simulated data. Further the real data from fluorescence imaging of stress fibres in mesenchymal human stem cells are evaluated. We apply model II which is inhomogeneous. The degree-of-fit testing of the model using various characteristics yields quite satisfactory results.

Planar Segment Processes with Reference Mark Distributions, Modeling and Estimation

“…This distribution can be also parametrized by a subjective choice of model, cf. [4]. In the present paper the main aim is to estimate the reference mark distribution non-parametrically, i.e.…”