Random Patterns and Structures in Spatial Data

Music City Center 

The useful information contained in spatio-temporal data is often represented in the form of geometric structures and patterns. The filaments or clusters of galaxies in our Universe are one such example.

There are two situations to consider. First, the pattern of interest is hidden in the data set, so the pattern must 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.

In this talk, Gibbs-marked point processes with interactions are presented for detection and characterisation of the patterns of interest. Classical and tailored MCMC samplers are presented to simulate the proposed models. Based on these ingredients, global optimisation and posterior sampling algorithms are built to perform statistical inference to detect and characterise the patterns of interest. Applications of the proposed approaches in astronomy, geology and network sciences are also shown.

marked Gibbs point processes with interaction

pattern detection and characterization in spatial data

MCMC simulation algorithms

Bayesian inference

spatial statistics, stochastic geometry

application domains: cosmology, environmental sciences, network sciences