What do Noisy Datapoints Tell Us About the True Signal?

Every measurement has uncertainty which needs to be quantified. Bayesian approaches achieve this naturally, by expressing results in terms of probabilities. I will give a conceptual overview of Bayesian analysis for metrological applications. This includes a discussion of Occam's razor, a helpful but qualitative dictum that is clarified and quantified when recast in the language of probability. Three example systems will illustrate these concepts: finding the true X-ray diffraction curve from noisy count data, interpolating the strain field of a stretched metal plate, and measuring aggregate uncertainty in flame speed datasets. All these systems require us to calculate probabilities for arbitrary smooth functions without assuming a functional form, and I will explain how to do this in a Bayesian context. Having quantified the uncertainty, I will also show several ways to represent it, including smooth animations of sequences of candidates for the true signal.

Speaker Bio: Dr. Charles R. ("Chip") Hogg obtained a M.S. and Ph.D. in Physics from Carnegie Mellon University in Pittsburgh, after earning a B.Sc. from Brock University in Canada with a double major in Computer Science and Physics. Since October 2010 he has been a Guest Researcher in the Ceramics Division at NIST, supported by a NIST-ARRA postdoctoral fellowship. He is broadly interested in applying Bayesian methods to the physical sciences; his recent work has heavily involved nonstationary Gaussian Processes with applications to local atomic structure determination.

Presentation Slides: PDF

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.