Agenda

Giada Adelfio, Università degli Studi di Palermo

The Zoom Room for the seminar is: https://unive.zoom.us/j/82776377762
Meeting ID: 827 7637 7762
Passcode: SanMarco1

Abstract:
Spatial, temporal, and spatio-temporal point processes, and in particular Poisson processes, are stochastic processes that are largely used to describe and model the distribution of a wealth of real phenomena.
When a model is fitted to a set of random points, observed in a given multidimensional space, diagnostic measures are necessary to assess the goodness-of-fit and to evaluate the ability of that model to describe the random point pattern behaviour. The main problem when dealing with residual analysis for point processes is to find a correct definition of residuals. Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data into residuals as a result of a thinning or a rescaling procedure. We alternatively consider here second-order statistics coming from weighted measures. Motivated by Adelfio and Schoenberg (2010) for the spatial case, we consider here an extension to the spatio-temporal context in addition to focussing on local characteristics.
Then, rather than using global characteristics, we introduce local tools, considering individual contributions of a global estimator as a measure of clustering. Generally, the individual contributions to a global statistic can be used to identify outlying components measuring the influence of each contribution to the global statistic.
In particular, our proposed method assesses goodness-of-fit of spatio-temporal models by using local weighted second-order statistics, computed after weighting the contribution of each observed point by the inverse of the conditional intensity function that identifies the process.
Weighted second-order statistics directly apply to data without assuming homogeneity nor transforming the data into residuals, eliminating thus the sampling variability due to the use of a transforming procedure. We provide some characterisations and show a number of simulation studies.
This presentation is based on the work published in Adelfio et al (2019), Stochastic Environmental Research and Risk Assessment, 
https://link.springer.com/article/10.1007/s00477-019-01748-1

Bio Sketch:
Giada Adelfio is an Associate Professor in Statistics at the University of Palermo. She holds a Master degree and a PhD In Statistics from the same University.