Observational Tests for the Cosmological Principle and World Models

We review observational tests for the homogeneity of the Universe on large scales. Redshift and peculiar velocity surveys, radio sources, the X-Ray Background, the Lyman-$\alpha$ forest and the Cosmic Microwave Background are used to set constraints on inhomogeneous models and in particular on fractal-like models. Assuming the Cosmological Principle and the FRW metric, we estimate cosmological parameters by joint analysis of peculiar velocities, the CMB, cluster abundance, IRAS and Supernovae. Under certain assumptions the best fit density parameter is Omega_m = 1 - lambda \approx 0.4 . We present a new method for joint estimation by combining different data sets in a Bayesian way, and utilising `Hyper-Parameters'.