Latent Variable Models in Statistics

In statistical terminology, a latent variable is a variable that is part of a studied system but for which no measurements can be obtained. Latent variable models are statistical models that account for such variables in their specification. While these models allow one to correct for the effects of latent variables, they lead to complicated dependencies among the observed variables. As a result, numerous challenges arise ranging from questions of parameter identifiability to model selection. In this talk we will discuss some of these challenges in the context of linear structural equation models, which exhibit algebraic-geometric structure that inspires solutions to the aforementioned statistical problems.