Houman Owhadi - California Institute of Technology, ACM Although numerical approximation and statistical inference are traditionally seen as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. We explore these connections in the setting of multiscale analysis and elliptic PDEs. Various parts of this talk are based on joint work with Florian T. Schäfer, Clint Scovel, Tim Sullivan and Gene R. Yoo.