You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Copy file name to clipboardExpand all lines: _posts/2024-11-18-Conditioning_joint_gaussian_on_sum.md
+5-1Lines changed: 5 additions & 1 deletion
Display the source diff
Display the rich diff
Original file line number
Diff line number
Diff line change
@@ -74,4 +74,8 @@ thus proving the first result.
74
74
75
75
Note that both $v$ and $A$ do not depend at all on $s$ and can be pre-calculated. The entries of $v$ are all on the interval $[0,1]$ and, in fact, form a simplex (their values sum to $1$). The posterior mean is always updated to be exactly consistent with the observed sum.
76
76
77
-
Assuming $\Sigma$ is rank $n$, $A$ has rank $n-1$ with exactly one "near-zero" eigenvalue. Additionally, the updated covariance become degenerate (singular), also with rank $n-1$. The updated covariance matrix is always "shrunk," so that the uncertainty is reduced in the posterior distribution.
77
+
Assuming $\Sigma$ is rank $n$, $A$ has rank $n-1$ with exactly one "near-zero" eigenvalue. Additionally, the updated covariance become degenerate (singular), also with rank $n-1$. The updated covariance matrix is always "shrunk," so that the uncertainty is reduced in the posterior distribution.
0 commit comments