Speaker(s): {Radu Stoica}

Date: Thursday 11th of April 2019

Location: room G201, ENSG, Nancy


Spatial data are sets of observations made of elements having two components. The first component gives the coordinates where the observation took place. The second component, represented usually by a multi-dimensional real vector, represents the measures associated at the corresponding location. Digital images, environmental data in epidemiology or catalogues of celestial bodies in astronomy are some typical examples of spatial data.
The spatial character of the data induces a strong morphological component to the possible answers that may be given to questions arising from the data analysis. This explains why the question almost always arising is what is the pattern hidden in the data ?
The main assumption of our work is that the pattern we are looking for is made of random objects that interact.
Marked point processes are a probabilistic tool able to model random configurations of interacting objects. The main difficulty with these models is that they do not always exhibit a precise analytical form for their normalising constants. Hence sampling from such a probability density requires adapted MCMC simulation. Within this framework, statistical inference can be done,using methods such as the simulated annealing algorithm, the Monte Carlo maximum likelihood, permutation tests and bootstrap methods.
The aim of this talk is to introduce marked point processes and to illustrate their applications with examples and data sets coming from : cosmology, image analysis and environmental sciences.