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DESCRIPTION:Title: Ergodic theory in data assimilation\n\nAbstract: Data as
 similation describes the method of blending dynamical models and observati
 onal data\, with the objective of reducing uncertainty in state estimation
  and prediction. The procedure has an ’optimal’ Bayesian solution\, which 
 tends to be computationally intractable for high dimensional models. As a 
 consequence\, many approximation procedures\, called approximate filters\,
  have been developed in the geoscience and numerical weather prediction co
 mmunities\, where models tend to be very high dimensional\, and where stat
 e estimation and uncertainty quantification are central tenets. It is impo
 rtant that we judge these approximations on how well they inherit importan
 t features from the true Bayesian solution. In this talk\, we will investi
 gate ergodicity for several types of filters that are prevalent in numeric
 al weather prediction. Ergodicity is of crucial importance for filters\; i
 t implies a robustness with respect to initial perturbations in state appr
 oximations\, moreover it suggests that the filter\, which is a proxy for t
 he true underlying dynamical system\, is inheriting important physical sta
 tistical properties. Alongside mostly positive results\, we will see that 
 approximate filters don’t always do a good job of inheriting ergodicity. W
 e define a class of models\, which are highly stable (and certainly ergodi
 c) for which well trusted approximate filters exhibit strong sensitivity t
 o initialization. In other words\, the filters quickly lose touch with rea
 lity. This talk is based on several joint works with Andy Majda\, Andrew S
 tuart\, Xin Tong\, Eric Vanden-Eijnden and Jonathan Weare.\n
DTSTART:20161215T200000Z
DTEND:20161215T200000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:David Kelly - Courant Institute
URL:/mathstat/channels/event/david-kelly-courant-insti
 tute-264738
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