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The correlation matrix (also called second moment) of an random vector is an matrix whose (i,j) th element is the correlation between the i th and the j th random variables.
Estimation of MVAR coefficients is based on calculation of the correlation matrix between channels R ij of k signals X i from multivariate set, [19] separately for each trial. The resulting model coefficients are based on the correlation matrix averaged over trials. The correlation matrix has the form:
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
With any number of random variables in excess of 1, the variables can be stacked into a random vector whose i th element is the i th random variable. Then the variances and covariances can be placed in a covariance matrix, in which the (i, j) element is the covariance between the i th random variable and the j th one.
When these expressions are combined into a matrix with i, j element (,), the result is a k × k positive-semidefinite covariance matrix of rank k − 1. In the special case where k = n and where the p i are all equal, the covariance matrix is the centering matrix .
Bayesian hierarchical modeling often tries to make an inference on the covariance structure of the data, which can be decomposed into a scale vector and correlation matrix. [3] Instead of the prior on the covariance matrix such as the inverse-Wishart distribution , LKJ distribution can serve as a prior on the correlation matrix along with some ...
In statistics, the Matérn covariance, also called the Matérn kernel, [1] is a covariance function used in spatial statistics, geostatistics, machine learning, image analysis, and other applications of multivariate statistical analysis on metric spaces.
The (potentially time-dependent) autocorrelation matrix (also called second moment) of a (potentially time-dependent) random vector = (, …,) is an matrix containing as elements the autocorrelations of all pairs of elements of the random vector .