Abstract
The useful information contained in spatio-temporal data is often
represented by geometric structures and patterns. The filaments or
clusters of galaxies in our Universe are one such example.
Two situations need to be considered. First, the pattern of interest
is hidden in the data set, so the pattern has to be detected. Second,
the structure of interest is observed, so a relevant characterisation
of it should be performed.
Probabilistic modelling and Bayesian statistical inference are
approaches that can provide answers to these questions.
This talk presents the use of Gibbs marked point processes for the
detection and characterisation of such structures. Marked point
processes with interactions are used to model the pattern of interest.
The proposed models are well defined and locally stable. Tailored to the
model, Monte Carlo and also exact algorithms are discussed to simulate
the proposed models. Based on these ingredients, a global optimisation
and a posterior sampling algorithms are presented to detect and
characterise the pattern of interest, respectively.
Application examples from astronomy and environmental sciences are also
shown.
