Algebraic geometry of hidden variable models in statistics

Algebraic statistics lies on the intersection of algebraic geometry and statistics. It is built on the observation that many fundamental models in statistics can be characterized and studied through algebraic geometry. This is also the case for hidden variable models that are widely used in statistics. Hidden variables usually represent quantities that cannot be measured directly. These models are complex and often their statistical behaviour can be explained by geometric properties. The main objective of this project is the study of hidden variable models using algebro-geometric methods. We aim to tackle questions related to identifiability, semialgebraic descriptions, and maximum likelihood estimation. Our goal is to develop general methods and theory for small hidden variables models without making simplifications to the model assumptions. We expect this theory to be fundamental in its own right and to yield insight into more general cases.