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FRINATEK-Fri prosj.st. mat.,naturv.,tek

Model selection and model verification for point processes

Alternative title: Valg og verifisering av modeller for punktprosesser

Awarded: NOK 6.2 mill.

The Challenge: Point processes are a class of statistical models used to describe data that can be viewed as points in time, space or space-time. Examples include earthquakes, plant and cellular systems, and animal colonies. Point process models are complicated by the varying high dimensionality of the data--if a point is added or removed from an observed point pattern, the dimensionality of the data set changes accordingly. Combined with intricate interactions between the data points, this results in many models having densities with intractable normalizing constants. Consequently, standard inference methods such as maximum likelihood are often not feasible. The objective of this project was to develop new data analysis methods for point process data with a focus on methods that are driven by and enable the comparison of competing scientific hypothesis for the data generating process. The Approach: We have focused on cluster point processes due to their importance in many applied settings. A common modeling framework for cluster point processes consists of three parts: A model for the parent process, a model for the cluster sizes, and a model for dispersion of the offspring around the parent. This hierarchical structure with potentially hidden layers (the parent process is e.g. commonly not observed) is particularly well suited for Bayesian inference approaches. We have developed new methodology for inferring latent model components, as well as for selecting the most appropriate model for a given data set using Bayesian and decision theoretic principles. The Results: With a focus on commonalities in methodology, we have been able to provide new insights for applications as diverse as detection of neuropathy, understanding of art appreciation and seal population assessment. We have published R software for Bayesian inference of cluster point processes for the model class of shot noise Cox processes and we have constructed new proper scoring rules for decision-theoretic coherent assessment of point process forecasts. Furthermore, we have organized a workshop bringing together leading experts in point process modelling to discuss the current state-of-the-art as well as the current open questions in this field.

Through the data analysis performed in the project, we have achieved new insights for the detection of neuropathy, understanding of art appreciation and seal population assessment. We have strengthened the interdisciplinary and international research collaborations of the project team, in particular that of the junior scientists who participated in the project. We anticipate that our software for Bayesian analysis of point process models will increase the use of such methods in practice and we expect that our new methods for validating point process forecasts will see wide use in point process forecasting, in particular in earthquake forecasting.

Many natural systems such as wildfires, disease occurrences, plant and cellular systems, and animal colonies are observed as point patterns in time, space or space and time. Point process methodology is thus applied by scientists in various fields to enhance their understanding of the underlying scientific phenomena behind their subject matter. In this research project, we propose to develop new methodology for Bayesian inference, model selection and validation of point process models to advance their use for investigating complex scientific hypotheses.

Publications from Cristin

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FRINATEK-Fri prosj.st. mat.,naturv.,tek