spectrum is not simple.

Nonlinearity in the gravitational evolution distorts the power spectrum on small scales ${\lower.5ex\hbox{{$\; \buildrel < \over \sim \;$}}}10{{\hbox {$\,h^{-1}$}{\rm Mpc}} }$. Peculiar velocities anisotropically distort the power spectrum on all scales. Spatial variation of the mass-to-light ratio or the galaxy biasing distorts the power spectrum. In deep redshift surveys, the spatial curvature and the evolution of the Hubble parameter distort the apparent pattern of the galaxy clustering. These various distortions in the observed power spectrum also depend on the cosmological model. Even if one can invent and adopt some ansatz on such a complex inversion problem, fair amount of information will be lost in this inversion process.

However, the reconstruction of the underlying power spectrum is not necessary to discriminate the cosmological models. In the Bayesian approach, the posterior probability of the set of model parameters ${{\mit \Theta}}= \{\theta_\alpha\}$, given a set of observational data $D =
\{d_i\}$ and additional prior information $I$, is estimated by Bayes’s theorem: $$P\left({{\mit \Theta}}|D,I\right) =
   P\left({{\mit \Theta}}|I\right) 
   \frac{P\left(D|{{\mit \Theta}},I\right)}
      {P\left(D|I\right)}.
\label{eq2-1}$$ The first factor is the Bayesian prior, i.e., the prior knowledge on the model parameters, and the denominator is the normalization constant. Evaluating the numerator is the crucial part 