HORAIRE
[ English ]
Programme préliminaire
Il y aura 6 conférences. Deux conférences seront données par Rasmus Waagepetersen, un professeur CANSSI invité. Chaque présentation sera d'une durée de 40 minutes, suivi d'une période de discussion de 10 minutes. L'atelier débute à 9:00 et se termine à 16:30.
- [09:30-10:50] Café d’accueil
[10:00-10:50] Jean-François Coeurjolly (UQAM).
Introduction to spatial point processes.
Abstract: I will begin by summarizing spatial point processes; namely how to theoretically characterize a point process, how to define its main componentssuch as its intensity functions and conditional intensities and how to use summary characteristics like the Ripley's $K$ function and the pair correlation function. I will briefly review the main statistical models for point patterns. My talk will highlight several examples and recent applications from different research areas (e.g. forestry, sports sciences, eye-movement data).
[10:50-11:40] Rasmus Waagepetersen (Aalborg University, Denmark).
Talk 1. Estimating functions with a view toward spatial statistics
Abstract: Maximum likelihood inference is in general considered superior in terms of statistical efficiency but in many contexts it can be very difficult to compute the likelihood function. Deterministic numerical or Monte Carlo approximations of the likelihood function may further lead to loss of efficiency for the resulting approximate maximum likelihood estimate. In this talk we review computationally simple alternative estimating function approaches available when first- and second-order moment properties are known for the data generating mechanism. We consider optimality of estimating functions and the special case of quasi-likelihood, and we discuss specific examples of estimating functions in statistics for spatial point patterns.
[11:50-13:30] Pause déjeuner
- [13:30-14:20] Patrick Brown (St. Michael's Hospital and Department ofStatistical Sciences, University of Toronto).
Bashing spatio-temporal point processes into the EMS algorithm
Résumé: Modelling regional case counts as an aggregated or censored continuous spatial point process is a conceptually simple model, with point locations being a latent variable and the continuous intensity surface being a (transformed) Gaussian random field. Inference for this process is extremely computationally intensive, as integrating out the uncertainty in case locations is a non-trivial task. The EMS algorithm, originally proposed by Silverman in 1990, is a fast and convenient exception. This talk will show how the EMS algorithm is equivalent to assuming point locations are a root-Gaussian Cox process subject to certain caveats. Interpreting EMS this way provides a natural way of using sparse matrices with a Gaussian Markov Random Field approximation to the Matern correlation. Joint work with Li Ka Shing.
[14:20-15:10] Daniel Simpson (University of Bath/ University of Toronto).
Sometimes care is needed to avoid pointless processes
Résumé: Spatial point processes have become a vital part of a spatial statistician's bag of tricks. In this talk, I will go through some of the challenges associated with using point processes within a more complex model and outline some of the questions that we need to keep in mind when using these models. Time permitting, I may even give some partial answers.
This is joint work with Janine Illian, Sigrunn Sørbye, and Gavin Shaddick.
- [15:10-15:30] Pause café
- [15:30-16:20] Rasmus Waagepetersen (Aalborg University, Denmark).
Talk 2. Orthogonal series estimation of the pair correlation function of a spatial point process
Résumé: The so-called pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Computation of a non-parametric estimate of the pair correlation function is a typical initial step of a statistical analysis of a spatial point pattern. Kernel estimates are popular non-parametric estimates but especially for clustered point patterns suffer from bias for small spatial lags. We introduce a new orthogonal series estimate which is much less biased for clustered point patterns. We consider consistency and asymptotic normality of the new estimate and also finite sample properties in a simulation study. Estimates are finally compared in an application to a data set of tropical rain forest tree locations.