Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have a multivariate linear-gaussian model and I am trying to estaimte a particular scalar set of parameters of the model.

I know how to derive the MLE in order to find the matrices A and Q (linear transfer function and covariance respectively).

I take the log of the joint distribution, find the above parameter derivatives, equal the expression to zero and solve for each of the 2 above parameters. The expression for A only depends on the data. The expression of Q depends on A and on the data. So I solve A first and then I can solve Q.

However, I have a specific application where I do not want to estimate the entire matrix A. Some scalar elements of the matrix I know a priori and some other scalar elements are the parameters to be estimated.

This is where my problems start:

1- The matrix calculus gets very hairy and I do not know how to solve this symbolically.

2- I tried to skip the step above and expanded the linear equation into a scalar expression with Matlab Symbolic toolbox since the parameters to be estimated are now scalars. I then went through Matlab differentiation and solving tools as well. It seems to work in principle.

3- On the original problem (the one I know how to solve), the expressions for A do not depend on Q. But now the Matlab solution shows that my estimated scalar Aij parameters do depend on Q and I believe it is correct. So now I have a set of parameters that all depend on each other and I am not sure what to do to solve them.

Any light on what I might need here would be appreciated.

Regards,

Carlos

BTW. this is my first post here, how do I insert latex expressions in these posts?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linear Gaussian parameter estimation

Loading...

Similar Threads - Linear Gaussian parameter | Date |
---|---|

A Error estimation in linear regression | Monday at 8:18 AM |

I ANOVA and Linear Regression Resource | Mar 2, 2018 |

Gaussian process with linear correlation | Jan 28, 2012 |

What is a non-linear gaussian? | Oct 6, 2009 |

How to prove the output of Linear Filtering a Gaussian Process is still Gaussian? | Aug 4, 2005 |

**Physics Forums - The Fusion of Science and Community**