Inhomogeneous interacting marked point processes for studying morphostructures in paleobiological data
Abstract
This paper presents inhomogeneous marked point processes with interactions that are applied
to the analysis of morphostructures exhibited by a paleo-biological dataset presented in Kolesnikov
(2018). Specifically, due to the nature of the dataset, we model the probability density function
describing the models by considering three effects: the distance to the nearest edge, the distance
to the lower right corner, and the distance to a reference circle. Furthermore, interactions between
the points through the observed marks are introduced. This is done using the Strauss and Area-
Interaction processes. Such models have four parameters that must be estimated. The proposed
procedure is as follows. First, the sufficient statistics of the proposed model are computed from the
data. Then, posterior sampling of the parameters is performed using the ABC Shadow algorithm.
Next, the quality of the estimation is assessed by calculating the estimation errors and evaluating
the significance of the model parameters. Finally, the model is verified using a Global Envelopes test
from Myllymäki et al. (2017); Myllymäki M (2023).
The C++ library DRLib is the main programming tool used to perform model simulations, and
parametric statistical inference based on the ABC Shadow algorithm the R package spatstat is used
for the exploratory analysis, for the model verification analysis by global envelope tests and for the
graphical presentation of the results.
Domains
Statistics [math.ST]Origin | Files produced by the author(s) |
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