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1. θ is [θ_{0}, θ_{1}]^{T}and θ_{replicated}= [θ_{0}, θ_{0}, θ_{1}, θ_{1}]^{T}, further θ is a gaussian with mean m_{θ}and covariance matrix S.

2. V is [V_{1}, V_{2}, V_{3}, V_{4}]^{T}

3. N is [N_{1}, N_{2}, N_{3}, N_{4}]^{T}, further it has gaussian distribution with mean 0, and diagonal covariance matrix σ.

4. let r = diag(V)*(1+jθ_{replicated}) + N where p(r|v, θ) is a gaussian with mean diag(V)*(1+jθ_{replicated}) and diagonal covariance matrix σ

If I know r, how do I integrate p(θ)[(r-diag(V) - jdiag(V)θ_{replicated}]^{H}[(r-diag(V) - jdiag(V)θ_{replicated}]dθ?

I know p(θ)[(r-diag(V) - jdiag(V)θ]^{H}[(r-diag(V) - jdiag(V)θ]dθ -> if θ is not replicated would be tr(ASA) + (Am_{θ}+b)^{H}(Am_{θ}+b) where A is -jdiag(V), and b is r - diag(V), but how would this work with θ_{replicated}?

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# Matrix Integral of different size

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