I want to prove that multivariate normal distribution maximizes the entropy

Asked Sep 20 '20 at 10:56

Active Sep 20 '20 at 10:56

Viewed 200 times

I was going through probability higher than I am being taught I was trying this problem ,

Show that the multivariate normal distribution maximizes the entropy over all distributions with the same covariance matrix.

Can anyone tell me how to solve it?

asked Sep 20 '20 at 10:56

Pulkit Joshi

Explanations are available in these notes and in these notes – Ben Grossmann Sep 20 '20 at 11:07
I am stuck due to multi-variable constraints – Pulkit Joshi Sep 20 '20 at 11:12
I recommend that you begin by trying to generalize a proof for the single-variable case and then update your question to let us know where exactly in the proof you get stuck – Ben Grossmann Sep 20 '20 at 11:15
multivariate maximum entropy is discussed in this article https://www.sciencedirect.com/science/article/pii/S0047259X07001005 – develarist Sep 23 '20 at 17:29
hypothesis testing approach to multivariate maximum entropy for financial time series https://www.nature.com/articles/s41598-020-67536-y – develarist Sep 23 '20 at 17:32

0 Answers0