Flexible Perturbation Models for Robustness to Misspecification

Abstract:
In many applications, there are natural statistical models with interpretable parameters that provide insight into questions of interest. While useful, these models are almost always wrong in the sense that they only approximate the true data generating process. In some cases, it is important to account for this model error when quantifying uncertainty in the parameters. We propose to model the distribution of the observed data as a perturbation of an idealized model of interest by using a nonparametric mixture model in which the base distribution is the idealized model. This provides robustness to small departures from the idealized model and, further, enables uncertainty quantification regarding the model error itself. Inference can easily be performed using existing methods for the idealized model in combination with standard methods for mixture models. Remarkably, inference can be even more computationally efficient than in the idealized model alone, because similar points are grouped into clusters that are treated as individual points from the idealized model. We demonstrate with simulations and an application to flow cytometry.

–

For more information and an up-to-date schedule, please see https://stellar.mit.edu/S/course/IDS/fa19/IDS.190/

**Taking IDS.190 satisfies the seminar requirement for students in MIT’s Interdisciplinary Doctoral Program in Statistics (IDPS), but formal registration is open to any graduate student who can register for MIT classes. And the meetings are open to any interested researcher.   Talks will be followed by 30 minutes of tea/snacks and informal discussion.**