Random Projections and Ensemble Kalman Filter BTP Stage-II Full Report by Raaz Dwivedi Roll

We review the celebrated Johnson Lindenstrauss Lemma and some recent advances in the understanding of probability measures with geometric characteristics on R, for large d. These advances include the central limit theorem for convex sets, according to which the uniform measure on a high dimensional convex body1 has marginals that are approximately Gaussian. We try to combine these two results to provide a theoretical justification to the successful heuristic methods implemented in Ensemble Kalman Filters for high dimensional data by oceanographars, meteorologists, etc. 1A convex body in R is a compact, convex set with a non-empty interior.

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