For a multivariate normal vector partitioned into N blocks, the l-th cumulant of multiinformation density equals (l-1)!/2 times the trace of the l-th power of the block regression-coefficient matrix.
An Introduction to Multivariate Statistical Analysis
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Cumulants of multiinformation density in the case of a multivariate normal distribution
For a multivariate normal vector partitioned into N blocks, the l-th cumulant of multiinformation density equals (l-1)!/2 times the trace of the l-th power of the block regression-coefficient matrix.