In this project, I conducted Bayesian inference of sea ice thickness given a freeboard measurement from IceSat-2 satellite data. Coupled with a physical model incorporating the local densities of water, snow, and ice with the relationship between freeboard, ice thickness, and snow thickness, I computed a posterior on the ice thickness that generated a freeboard measurement of ten centimeters. In this process, I also used a hierarchical model to approximate the margin of error of IceSat-2's measurements.
To compute this non-conjugate, non-linear, analytically intractable posterior, I used the Metropolis-within-Gibbs technique with Markov Chain Monte Carlo to sample from the distribution. With this technique, I found the following marginal posterior distributions, and estimated an ice thickness of 1.34 meters with a standard deviation of 0.55 meters representing the remaining Bayesian uncertainty.
For details, see the project paper and the Jupyter notebook. Note: I have observed that the Jupyter notebook sometimes does not render properly on GitHub. If GitHub isn't rendering it right, go to https://nbviewer.jupyter.org/github/jeffzyliu/bayesian-sea-ice/blob/master/IceThickness.ipynb which will definitely provide a better render.
"Went above and beyond the level of problems we discussed... This is one of the best projects in the class."
- Dr. Matthew Parno, Adjunct Prof. @ Dartmouth, MATH 76: Introduction to Bayesian Computation
