Structured Additive Distributional Regression Models in Ecology and Forestry: Applications, Software, and Inference
PhD studentHannes Riebl
Research OutlineWe develop flexible regression models with an emphasis on applications in forestry and ecology, building on the so-called structured additive distributional regression model class. The models are designed in close collaboration with the ecologists and forest scientists in the RTG to address some of the empirical problems in these fields. We establish the statistical methodology for MCMC-based Bayesian inference, investigate the statistical properties of the models and inference algorithms, and develop interpretations for the specific research questions at hand.
Our first paper discusses a method for the analysis of high-resolution dendrometer measurements, which we use to study the intra-annual stem growth of 85 deciduous trees from Germany during the vegetation periods 2012 and 2013. The method embeds Gaussian processes (GPs) as continuous response structures in the distributional regression framework, where the parameters of both the mean and the covariance function of the GPs are linked to structured additive predictors with different types of covariate effects (linear, random, non-linear, spatial, …).
Another paper deals with the statistical assessment of the relationship between the site conditions and the species richness at a given research plot, taking into account that species richness measurements often represent underdispersed count data. We build a hierarchical model for the observed number of species and compare the performance of the new model to a number of alternatives, especially from the domain of structured additive distributional regression.
To facilitate our research on structured additive distributional regression models, we are developing LIESEL, a software framework for all components of the model class written in Python and based on JAX, a cutting-edge machine learning library for auto-differentiable and JIT-compilable NumPy functions. LIESEL provides the means to set up distributional regression models, structured additive predictors, and MCMC sampling schemes in a modular way. It also comes with an R interface, which further assists the user with the model configuration.
The long-term development of LIESEL will be funded by the German Research Foundation (DFG) for three years starting in October 2021.