Short assignment, due 3/26

Jeff wants you to prove this short preliminary result, due on Thursday, 3/26:

For a p-dimensional parameter \theta, if its density

g(\theta) \propto \exp\left[-\frac{1}{2}(\theta^T A \theta -2 b^T \theta)\right],

where A is a p \times p matrix and b a p \times 1 vector, then

\theta \sim N(A^{-1}b, A^{-1})

This is a commonly used technique called “completing the square,” in its general matrix form. It is often needed when working with the kernel of normal distributions (as we did later in the lecture today).

One Response to “Short assignment, due 3/26”

  1. Stat 295, 3/24/09 « BayesRules Says:

    […] BayesRules Just another weblog « Short assignment, due 3/26 […]

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