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  • $\begingroup$ getting stuck because $C_w \ne C_s$ ? $\endgroup$ Commented Dec 28, 2017 at 15:06
  • $\begingroup$ It's okay even if you take Cw and Cs as diagonal matrices! $\endgroup$ Commented Dec 28, 2017 at 15:09
  • $\begingroup$ so where stuck? $\endgroup$ Commented Dec 28, 2017 at 15:13
  • $\begingroup$ In calculating Pd and Pfa $\endgroup$ Commented Dec 28, 2017 at 15:14
  • $\begingroup$ try the scaler case first and then the independent case. The multidimensional integrals can be challenging. There are numerical papers using quadrature rules. There are some tricks in Abramawitz and Stegun. Chervov bounds can also be helpful $\endgroup$ Commented Dec 28, 2017 at 15:26