  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 < 0.48. Both
conclusions hold regardless of initial conditions.
