vector ${{\mbox{\boldmath $d$}}}$ into vector ${{\mbox{\boldmath $B$}}}$ of a smaller dimension: $${{\mbox{\boldmath $B$}}} = P {{\mbox{\boldmath $d$}}},
\label{eq2-4}$$ where the projection matrix $P$ has a dimension $M\times N$, and the dimension of the vector ${{\mbox{\boldmath $B$}}}$ is $M$, where $M < N$. The correlation matrix of the reduced data vector is given by $$C({{\mit \Theta}}) = 
  \left\langle
    \left({{\mbox{\boldmath $B$}}} - \left\langle {{\mbox{\boldmath $B$}}}
      \right\rangle_{{\mit \Theta}}\right) 
    \left({{\mbox{\boldmath $B$}}} - \left\langle {{\mbox{\boldmath $B$}}}
      \right\rangle_{{\mit \Theta}}\right)^{\rm T}
  \right\rangle_{{{\mit \Theta}}} =
  P R({{\mit \Theta}}) P^{\rm T}.
\label{eq2-5}$$ The linear transformation from ${{\mbox{\boldmath $d$}}}$ to ${{\mbox{\boldmath $B$}}}$ ensures the preservation of the Gaussianity of the distribution.

A clever choice of the projection matrix $P$ enables us to avoid the inversion of the originally huge correlation matrices without losing most of the information contained in signals. In such a case, the inversion of smaller correlation matrices for the reduced data suffices for the Bayesian analysis, and the computation time is reduced by a factor of about $(M/N)^{2.8}$. In Appendix \[app1\], the construction of the projection matrix by the KL eigenmodes with maximal signal-to-noise ratio is comprehensively reviewed. In short, the projection matrix by KL eigenmodes picks the first $M$ modes that have largest S/N ratio.

The 