Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix

<p style='text-indent:20px;'>We present an ensemble filtering method based on a linear model for the precision matrix (the inverse of the covariance) with the parameters determined by Score Matching Estimation. The method provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. The parameters are found by solving a system of linear equations. The analysis step uses the inverse formulation of the Kalman update. Several filter versions, differing in the construction of the analysis ensemble, are proposed, as well as a Score matching version of the Extended Kalman Filter.</p>

Covariance regularization for metabolomic data on the drought resistance of barley

SummaryModern chromatography largely uses the technique of gas chromatography coupled with mass spectrometry (GC–MS). For a set of data concerning the drought resistance of barley, the problem of the characterization of a covariance structure is investigated with the use of two methods. The first is based on the Frobenius norm and the second on the entropy loss function. For the four considered covariance structures – compound symmetry, three-diagonal and penta-diagonal Toeplitz and autoregression of order one – the Frobenius norm indicates the compound symmetry matrix and autoregression of order one as the most relevant, whilst the entropy loss function gives a slight indication in favor of the compound symmetry structure.

A Tapering Method in the Construction of Covariance Regularization

Estimation of Population covariance matrix from samples is important in a wide range of areas of statistical analysis. In the estimation, the sample covariance matrix, which is the most natural and standard estimator, often performs badly. With the collection of large high-dimensional data in scientific investigation, the related covariance matrix becomes complicated to deal with. Therefore, for the convenience in computing and analyzing, we need to simplify the covariance matrix. This method is referred as regularization. In this paper, we will consider a proof for a construction of covariance regularization by tapering.