Hierarchical Bayesian Regression Models with Applications in Ecology and Forestry
PhD studentJens Lichter
Research OutlineWe focus on the development of Hierarchical Bayesian regression models and fast inferential methods for analysing highly complex system in the field of ecology and forestry. Our models include a hierarchical structuring of model parameters and a flexible choice of possible covariate effects on the response, e.g. linear, nonlinear, random or spatial effects. The flexible model formulation enables a comprehensive analysis of variable relations in complex systems.
With increasing model complexity and large data sets, such as the high-resolution dentrometer data from our RTG plots, the parameter estimation can take high computationally times when using classical Markov Chain Monte Carlo (MCMC) methods. Therefore, we explore Variational Inference (VI) as fast inferential alternative for such models in our first project.
VI has already been applied to regression models, but with rather restrictive assumptions, leading to underestimation of parameter uncertainties. However, over the last decade many methods within VI have been developed using less restrictive assumptions. We focus on a VI method called Semi-Implicit VI to accurately estimate parameter uncertainties and implement the method in the programming language Python . We apply the method to inventory data from the Bundeswaldinventur to model tree height given covariates such as precipitation, altidute, temperature among other correlated covariates.
In the second project we analyze tree growth dynamics using dendrometer data from the Enrico plots. Hannes Riebl from the first cohort of subproject 10 has developed a versatile hierarchical distributional regression model that can be applied to model tree growth dynamics. In this model the complexity of the response structure is modeled as a Gaussian Process. As a next step, we want to further elaborate on the model by improving the efficiency of the implementation and by tailoring the model more specifically to the research question of how competition among tree species (Norway Spruce, European Beech, Douglas fir) and abiotic drivers influences tree growth dynamics. Additionally, we want to analyze how abiotic and biotic variables interact, how water status affects stem growth and how tree vitality can be predicted from previous growth patterns or water status.