Abstract
Groups and symmetries are at the heart of many problems in statistics and data analysis. I will focus on parameter estimation in statistical models via maximum likelihood estimation. We will see connections between maximum likelihood estimation, linear algebra, and invariant theory. The group or symmetric structure of a statistical model can be used to capture the existence and uniqueness of a maximum likelihood estimate, as well as to suggest suitable algorithms to find it. This talk is based on joint work with Carlos Améndola, Kathlén Kohn, Visu Makam, and Philipp Reichenbach.