Multivariate Gaussian Distribution
Consider the i.i.d. Gaussian variables , where
and . The random variables from a linear combination of , e.g.
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Mapping the real domain into a finite interval
How to construct ?
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Newton's method
To numerically find a root of , we may use the Newton’s method. Assuming
the root is at the proximity of , to find a better approximate ,
we consider the tangent line at , which is provided by the
equation
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Property of Matrix and Its Eigenvalues
For a matrix , and its eigenvalue
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Covariance & Correlation
Consider random variables and , to measure how much they change together, we use covariance:
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