We investigate in detail the question whether a non-vanishing cosmological constant is required by present-day cosmic microwave background and large scale structure data when general isocurvature initial conditions are allowed for .
We also discuss differences between the usual Bayesian and the frequentist approaches in data analysis .
We show that the COBE-normalized matter power spectrum is dominated by the adiabatic mode and therefore breaks the degeneracy between initial conditions which is present in the cosmic microwave background anisotropies .
We find that in a flat universe the Bayesian analysis requires \Omega _ { \Lambda } \neq 0 to more than 3 \sigma , while in the frequentist approach \Omega _ { \Lambda } = 0 is still within 3 \sigma for a value of h \leq 0.48 .
Both conclusions hold regardless of initial conditions .