  We study the Mott-insulator transition of bosonic atoms in optical lattices.
Using perturbation theory, we analyze the deviations from the mean-field
Gutzwiller ansatz, which become appreciable for intermediate values of the
ratio between hopping amplitude and interaction energy. We discuss corrections
to number fluctuations, order parameter, and compressibility. In particular, we
improve the description of the short-range correlations in the one-particle
density matrix. These corrections are important for experimentally observed
expansion patterns, both for bulk lattices and in a confining trap potential.
