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== Multivariate Normal == | == Multivariate Normal == | ||

- | For the Kalman lab, you will need to show multivariate normals. The following sample file shows how this should be done. Feel free to play around with the palette and isosamples settings. The complete file can be seen at [http://aml.cs.byu.edu/~kseppi/cs470sp07files/kalman.gpi kalman.gpi] and the image is available at [http://aml.cs.byu.edu/~kseppi/cs470sp07files/kalman.png kalman.png]. Note that the code given below uses sigma-x, sigma-y and rho (where rho (<math>\rho</math>) is the [[correlation]] between <math>X</math> and <math>Y</math>) to represent the covariance matrix which we called <math>\Sigma</math> in class. Remember that <math>\Sigma</math> is symmetric so we really only need three values to represent it. Thus any 2-d <math>\Sigma</math> can be represented by sigma-x, sigma-y and <math>\rho</math> as shown here: | + | For the Kalman lab, you will need to show multivariate normals. The following sample file shows how this should be done. Feel free to play around with the palette and isosamples settings. The complete file can be seen at [http://aml.cs.byu.edu/~kseppi/cs470sp07files/kalman.gpi kalman.gpi] and the image is available at [http://aml.cs.byu.edu/~kseppi/cs470sp07files/kalman.png kalman.png]. Note that the code given below uses sigma-x, sigma-y and rho (where rho ($\rho$) is the [[correlation]] between $X$ and $Y$) to represent the covariance matrix which we called $\Sigma$ in class. Remember that $\Sigma$ is symmetric so we really only need three values to represent it. Thus any 2-d $\Sigma$ can be represented by sigma-x, sigma-y and $\rho$ as shown here: |

- | :<math> | + | :$ |

\Sigma = | \Sigma = | ||

\begin{bmatrix} | \begin{bmatrix} | ||

Line 71: | Line 71: | ||

\rho \sigma_x \sigma_y & \sigma_y^2 | \rho \sigma_x \sigma_y & \sigma_y^2 | ||

\end{bmatrix}. | \end{bmatrix}. | ||

- | </math> | + | $ |

and as explained on [http://en.wikipedia.org/wiki/Multivariate_normal_distribution wikipedia] | and as explained on [http://en.wikipedia.org/wiki/Multivariate_normal_distribution wikipedia] |