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).

Advertisements

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

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

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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: