Targeted Machine Learning for the Integration of Mathematical, Numerical, and Statistical models: Integral Projection Models in Environmental Sciences

Within demographic ecology, integral projection models (IPMs) play an important role in translating models for individual life history into demographic projections about species viability, coexistence, and ecological management practice. Developing an IPM starts with data on individuals from which models are built for their growth, survival and reproduction from one time-period to the next. However, while developing these models often follow classical statistical approaches, there are limited tools to evaluate the uncertainty of the quantities often calculated from IPMS, or to guide model selection given that those quantities are of interest. In this talk we adapt the tools of targeted maximum likelihood estimation (tMLE) to IPMs. Originally developed for causal inference, tMLE methods treat the outcome of interest as a functional of the data distribution and then use the resulting influence function to both correct the bias in these estimates and provide uncertainty quantification. A benefit of this framework is that no structural assumptions need to be made on the model components so long as they exhibit sufficient convergence, allowing for the inclusion of nonparametric and machine learning tools within our toolbox. We will walk through the basic framework of tMLE and its applications to integral projection models particularly in the context of survey data from the Idaho Experimental Sheep Station, as well as pointing to the wide range of open problems and potential of new development. This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented during the talk.