Dipartimento di Scienze Statistiche

  Seminario DSS online nell'ambito del corso "Spatial Statistics and statistical tools for the environment"   Mercoledi' 3 dicembre ore 10.00   "Extending the latent Gaussian family using non linear term to account for the observation model"    Seminario online che si svolge  al link https://uniroma1.zoom.us/j/82679000208     Sara Martino Full Professor Department of Mathematical Sciences, NTNU Trondheim, Norway   Abstract This seminar provides an in-depth overview of Latent Gaussian Models (LGMs) and recent methodological advances that extend their applicability to settings involving non-linear predictors. LGMs constitute a broad and powerful class of Bayesian hierarchical models in which dependence structures are encoded through Gaussian latent fields, enabling flexible modelling of diverse data types—including spatial, temporal, and spatio-temporal processes. A central advantage of LGMs lies in their compatibility with the Integrated Nested Laplace Approximation (INLA), which offers a fast and accurate alternative to simulation-based Bayesian inference. However, classical INLA assumes that the predictor is a linear function of the latent Gaussian field, limiting its use in problems such as logistic growth dynamics, aggregation of continuously indexed fields, or thinned Poisson processes, where the observation model depends non-linearly on latent components. The seminar discusses why such non-linear predictors arise naturally in modern applied statistics and demonstrates how recent developments—implemented in the inlabru library—enable approximate INLA-based inference in these extended models. The approach relies on iterative linearisation via Taylor expansions, allowing non-linear observation models to be embedded within the LGM framework. Practical examples, convergence diagnostics, and considerations regarding prior specification and model interpretability are presented, highlighting both the potential and the challenges of this methodological extension.