Abstract:

Global climate model validation is integral for ensuring climate models produce realistic climatologies. However, many post-hoc statistical evaluation methods rely on simplifying models that discard information and fail to distinguish between different sources of variability. We introduce a functional data analysis approach for computing sliced amplitude and phase distances between spatiotemporal processes, inspired by the sliced Wasserstein distance. Because our method uses time-warping, which respects temporal ordering, we can more precisely quantify differences between climate models than the previous Wasserstein-based approach. Finally, we apply our method to compare the performance of CMIP5 vs. CMIP6 models in representing historical surface temperature and precipitation from 1979-2005.

Abstract:

This project aims to develop models for classifying documents utilizing compression analytics. Existing compression techniques such as Prediction by Partial Matching (PPM) and other Variable Order Markov Models are probability models for compressing documents. These type of lossless compression techniques are very valuable for compression though utilizes ad hoc approaches for unseen observations. Ad hoc methods such as using unique letters as counts for a smoothing technique. We propose to solve this problem by utilizing Bayesian Context Trees (BCTs) with smoothing techniques that utilizes variable length contexts and incorporating prior knowledge to estimate the probability distribution of various sequences as tree models. From there the BCT algorithm then identifies the maximum a posteriori tree model. Compression Analytics is a reduction in the number of bits needed to represent data. PPM’s escape method is used to help replace any missing values in the prediction stage. This smoothing technique is very useful in combining different order Markov Models though does lack some statistical properties. This is where BCTs can help fill in gaps of PPM.