Andrew Nguyen L&S Math & Physical Sciences
Recovering Signals with Confidence: Sparse Bayesian Mixture Modeling
In experimental sciences, effectively extracting “signals” hidden in noisy data is a constant challenge. Often, this data is “mixed” from several hidden subpopulations. For example, consider radii measurements of newly discovered exoplanets: we may not know how many distinct types of exoplanets exist, how common each type is, nor characteristics of each type (e.g., average radii).
Currently, a well-established method called Non-Parametric Maximum Likelihood Estimation (NPMLE) is capable of isolating these signals. However, it extends poorly into high-dimensional data and lacks “uncertainty quantification,” (UQ) meaning that it cannot tell scientists how confident it is in its own estimates.
My research addresses this gap by developing a novel Bayesian Gaussian Mixture Model to untangle these subpopulations and provide UQ. By encoding particular mathematical flexibilities and constraints into the model’s architecture, this project aims to match NPMLE’s accuracy, extend its performance into higher dimensions, and successfully quantify uncertainty, allowing scientists to trust the signals they recover from their data.
Message To Sponsor
Thank you for your support! I have grown very interested in Bayesian Statistics and deeply appreciate the opportunity to deeply involve myself in research this summer. I particularly like the theoretical portions of this project, as I intend to pursue doctoral studies in this field. Thank you again for the opportunity to spend my summer deeply immersed in research; I can't wait to share what I find.