Explore tensors in statistics and data analysis in this comprehensive lecture by Anna Seigal from the University of Oxford. Delve into various tensor applications, including probability tensors, biological measurement tensors, and signature tensors for encoding time-series data. Examine tensor decompositions and their algebraic properties. Learn about probability tensors, conditional independence equations, hidden variables, parameter estimation, and the 'best' rank one approximation. Investigate moments, cumulants, and the signature of paths. Gain insights into advanced mathematical concepts and their practical applications in data science and statistics through this in-depth tutorial, part of the "Tensor Methods and Emerging Applications to the Physical and Data Sciences" series organized by the Institute for Pure & Applied Mathematics at UCLA.