Topological data analysis allows geometric and topological constructions to be imported into the study of data. A central idea of this methodology is to determine features which persist as a single parameter varies across multiple scales. We consider a generalized version of persistence in which multiple parameters can vary simultaneously, inspired by geometric and differential topology. Our construction arises from one-parameter families of smooth functions on compact manifolds. I will show how to analyse this version of multiparameter persistence in geometric terms with several examples. I will also comment on a practical application of this work in terms of parameter estimation, e.g., bandwidth selection for kernel density estimation. This is joint work with Peter Bubenik.