I want to calulate the likelihood by evaluating the second integral , I am supposed to get the third step but I don't seem to get it , how do I evaluate the integra l
2026-04-01 16:53:23.1775062403
Integrating multivatiate gaussian for likelihood
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The related conclusion and derivation can be found in PRML Chapter 2.3.3.
The derivation there avoids the integral. We can first obtain the joint distribution of $(Z, Y)$ through the covariance matrix in Eqn. (2.105) and the expectation in Eqn. (2.108), and then simply pick the expectation and variance of $Z$, which induces the density in your third step.