Generalized variance

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The generalized variance is a scalar value which generalizes variance for multivariate random variables. It was introduced by Samuel S. Wilks.

The generalized variance is defined as the determinant of the covariance matrix, $\det(\Sigma )$ . It can be shown to be related to the multidimensional scatter of points around their mean.^[1]

Minimizing the generalized variance gives the Kalman filter gain^[2].

References

^ Kocherlakota, S.; Kocherlakota, K. (2004). "Generalized Variance". Encyclopedia of Statistical Sciences. Wiley Online Library. doi:10.1002/0471667196.ess0869. ISBN 0471667196. Retrieved 30 October 2019.
^ Proof that the Kalman gain minimizes the generalized variance, Eviatar Bach https://arxiv.org/abs/2103.07275

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[1] Kocherlakota, S.; Kocherlakota, K. (2004). "Generalized Variance". Encyclopedia of Statistical Sciences. Wiley Online Library. doi:10.1002/0471667196.ess0869. ISBN 0471667196. Retrieved 30 October 2019.

[2] Proof that the Kalman gain minimizes the generalized variance, Eviatar Bach https://arxiv.org/abs/2103.07275

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