Introduction and Primer

Start with a unit circle. End with a Bivariate Normal.

• U is a n x 2 matrix containing n random draws from the uniform circle.
• UA is the result of the matrix multiplication between n x 2 U and 2 x 2 A, the Cholesky decomposition of a 2x2 matrix Q.
  • A makes a circle (U) into an ellipse (UA)
  • A can be thought of as a “square root” of a matrix. A’A = Q.
• When R $\sim \chi$(df=2) distribution, RUA is the bivariate normal distribution G(0,Q), Equivalently
  • mvpd uses G for Gaussian