# Difference between revisions of "Segment 17. The Multivariate Normal Distribution"

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The direct YouTube link is [http://youtu.be/t7Z1a_BOkN4 http://youtu.be/t7Z1a_BOkN4] | The direct YouTube link is [http://youtu.be/t7Z1a_BOkN4 http://youtu.be/t7Z1a_BOkN4] | ||

− | Links to the slides: [http:// | + | Links to the slides: [http://wpressutexas.net/coursefiles/17.MultivariateNormal.pdf PDF file] or [http://wpressutexas.net/coursefiles/17.MultivariateNormal.ppt PowerPoint file] |

===Problems=== | ===Problems=== | ||

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[[Media:somematrices.txt|Some 3x3 Matrices]] | [[Media:somematrices.txt|Some 3x3 Matrices]] | ||

− | [http:// | + | [http://wpressutexas.net/coursewiki/images/f/f4/Multivar_normal.pdf MVN Exercise] |

[[Media:MultivarGaussExample.nb.txt|Bill's Mathematica notebook for problem 2 (above)]]. (Download file, rename as MultivarGaussExample.nb, then open in Mathematica.) | [[Media:MultivarGaussExample.nb.txt|Bill's Mathematica notebook for problem 2 (above)]]. (Download file, rename as MultivarGaussExample.nb, then open in Mathematica.) |

## Latest revision as of 14:34, 22 April 2016

#### Watch this segment

(Don't worry, what you see statically below is not the beginning of the segment. Press the play button to start at the beginning.)

{{#widget:Iframe |url=http://www.youtube.com/v/t7Z1a_BOkN4&hd=1 |width=800 |height=625 |border=0 }}

The direct YouTube link is http://youtu.be/t7Z1a_BOkN4

Links to the slides: PDF file or PowerPoint file

### Problems

#### To Calculate

1. Calculate the Jacobian determinant of the transformation of variables defined by

2. Consider the 3-dimensional multivariate normal over with and

. (Note the matrix inverse notation.)

What are 2-dimensional and for

(a) the distribution on the slice ?

(b) the marginalization over ?

Hint: The answers are all simple rationals, but I had to use Mathematica to work them out.

#### To Think About

1. Prove the assertions in slide 5. That is, implement the ideas in the blue text.

2. How would you plot an error ellipsoid in 3 dimensions? That is, what would be the 3-dimensional version of the code in slide 8? (You can assume the plotting capabilities of your favorite programming language.)

#### Class Activity

Bill's Mathematica notebook for problem 2 (above). (Download file, rename as MultivarGaussExample.nb, then open in Mathematica.)