Agenda

Dani Gamerman
Universidade Federal do Rio de Janeiro

Abstract

The advance of Bayesian statistics has grown considerably in the last decades leading to models with increasing complexity. This growth was accompanied by the need for approximations and we became used to them. Some of them are computational for extraction of information from the posterior distribution but other approximations are caused by the assumed inability to handle the models as they were posed.

One important example is provided by point patterns (PP). This is one of the most commonly encountered data structure in spatial analysis, where locations of occurrences of a certain phenomenon of interest are observed. Estimation of the intensity of occurrence is the primary interest in the many usual settings. Nevertheless, the likelihood of the non-parametric intensity is not available analytically. Approximations are usually applied, inducing biases and losses in all likelihood-based inferential procedures. This inefficiency is inherited by all models that contain PP components.
Further complexity is brought by the use of Gaussian processes (GP) to induce smoothness over the intensity function.

This talk will address these complications and will propose exact procedures to remedy the situation.
These procedures are based on augmentation with latent processes and, more importantly, avoid model approximations.

This idea opens up a framework to handle a variety of models involving PP components without compromising their integrity. Examples include the use of PP regression with space-varying coefficients, geostatistics with sampling preferentiality, analysis of presence-only data in Ecology and nonstationary/discontinuous intensity functions. Different augmentation processes were required for the above contexts. Results from tests with synthetic data, comparison against alternatives and applications to real data are presented.

Issues associated with cost of computation with GP, parallelization and software are briefly addressed.

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This lecture is included in the programme of the 2024 ISBA World Meeting

For further information please contact isba2024@unive.it