Date: Friday, October 28, 2022

Time: 1:00 – 2:00 pm

Location: HP 4351 (MacPhail Room), Carleton University

Title: Covariance estimation for filtering in high dimension

Speaker: Marie Turcicova (Carleton University)

**Abstract**: Estimating large covariance matrices from small samples is an important problem in many fields. Among others, this includes spatial statistics and data assimilation, which provides the main motivation for methods discussed in this seminar. We will have a look at several methods of covariance estimation with emphasis on regularization and covariance models useful in filtering problems. In the first part of the seminar, we will see a brief summary of basic covariance estimating methods used in data assimilation. Then, the attention is shifted to nested covariance models with distinct type of hierarchy. Parameters of these models can be estimated by the maximum likelihood method, but for more complex covariance models, this method cannot provide explicit estimators. In the case of a linear model for a precision matrix (inverse of the covariance matrix), however, consistent estimator in a closed form can be computed by the score matching method. In the second part of the seminar, we will have a look at the basic filtering algorithms that are used for data assimilation and also two new filtering algorithms, where the covariance matrix is estimated by the score matching method, are shown. This talk is based on the doctoral thesis of the speaker.