Department of Mathematical Sciences, Aarhus University

Room Koll.G, 1532-214

**Abstract:** Traditionally, model selection methods for point processes mainly aim at detecting repulsion or clustering in the point pattern and there seems to be a lack of methods that apply beyond this initial distinction. In this talk, we discuss how Bayesian methodology might be applied to fill this gap. We give a short review of previous work in this direction and show how Bayes factors can be used to determine model probabilities for simple models without performing a full inference under each model. For more complicated models, this is usually no longer the case as the marginal likelihoods for the competing models cannot be computed directly. Here, we propose reversible jump algorithms that can be used to determine the model probabilities.

Joint work with Peter Guttorp (University of Washington).

**Abstract:** Many observed spatial point patterns contain points placed roughly on line segments. Point patterns exhibiting such structures can be found for example in archaeology (locations of bronze age graves in Denmark) and geography (locations of mountain tops). We consider a particular class of point processes whose realizations contain such linear structures. This point process is constructed sequentially by placing one point at a time. The points are placed in such a way that new points are often placed close to previously placed points, and the points form roughly line shaped structures. We consider Markov chain Monte Carlo based estimation of parameters and missing data (the order in which the points has appeared is missing) for this class of point processes in a Bayesian setup. This is exemplified by real data.

Joint work with Jesper Møller (Aalborg University).

**Abstract:** We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on

the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across

outcomes and the spatial correlation structure, thereby allowing for adaptive smoothing and spatial autocorrelation parameters. Our methods are illustrated using simulated and real-world examples, including an application to cancer mortality surveillance.

Joint work with Adrian Dobra (University of Washington) and Abel Rodriguez (University of California, Santa Cruz).