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In statistics, the precision matrix or concentration matrix is the matrix inverse of the covariance matrix or dispersion matrix, =. [ 1 ] [ 2 ] [ 3 ] For univariate distributions , the precision matrix degenerates into a scalar precision , defined as the reciprocal of the variance , p = 1 σ 2 {\displaystyle p={\frac {1}{\sigma ^{2}}}} .
GLS is employed to improve statistical efficiency and reduce the risk of drawing erroneous inferences, as compared to conventional least squares and weighted least squares methods. It was first described by Alexander Aitken in 1935. [1] It requires knowledge of the covariance matrix for the residuals. If this is unknown, estimating the ...
More technically, general versions of the approximation lead to a sparse Cholesky factor of the precision matrix. Using the standard Cholesky factorization produces entries which can be interpreted [2] as conditional correlations with zeros indicating no independence (since the model is Gaussian). These independence relations can be ...
In Bayesian statistics, the Jeffreys prior is a non-informative prior distribution for a parameter space.Named after Sir Harold Jeffreys, [1] its density function is proportional to the square root of the determinant of the Fisher information matrix:
In statistics, the graphical lasso [1] is a sparse penalized maximum likelihood estimator for the concentration or precision matrix (inverse of covariance matrix) of a multivariate elliptical distribution.
Matrix Toolkit Java is a linear algebra library based on BLAS and LAPACK. ojAlgo is an open source Java library for mathematics, linear algebra and optimisation. exp4j is a small Java library for evaluation of mathematical expressions. SuanShu is an open-source Java math library. It supports numerical analysis, statistics and optimization.
OpenEpi is a free, web-based, open source, operating system-independent series of programs for use in epidemiology, biostatistics, public health, and medicine, providing a number of epidemiologic and statistical tools for summary data.
In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a multivariate normal distribution.