Bayesian estimation of the observation‐error covariance matrix in ensemble‐based filters

Estimation of Covariance Matrix

Estimation of population covariance matrices from samples of multivariate data is important. (1) Estimation of principle components and eigenvalues. (2) Construction of linear discriminant functions. (3) Establishing independence and conditional independence. (4) Setting confidence intervals on linear functions. Suppose we observed p dimensional multivariate samples X1, X2, · · · , Xn i.i.d. wi...

Bayesian Hierarchical Model for Large-Scale Covariance Matrix Estimation

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our ap...

Estimation of Covariance Matrix in Signal Processing When the Noise Covariance Matrix is Arbitrary

Covariance Matrix Estimation in Time Series

Covariances play a fundamental role in the theory of time series and they are critical quantities that are needed in both spectral and time domain analysis. Estimation of covariance matrices is needed in the construction of confidence regions for unknown parameters, hypothesis testing, principal component analysis, prediction, discriminant analysis among others. In this paper we consider both l...

Bayesian Filters for Location Estimation

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