  We study the short-range coherence of ultracold lattice Bose gases in the
Mott insulating phase. We calculate the visibility of the interference pattern
and the results agree quantitatively with the recent experimental measurement
[Phys. Rev. Lett. 95, 050404 (2005)]. The visibility deviation from the
inversely linear dependence on the bare on-site interaction U_0 is explained
both in smaller and larger U_0. For a smaller U_0, it comes from a second order
correction. For a larger U_0, except the breakdown of adiabaticity as analyzed
by Gerbier et al, there might be another source to cause this deviation, which
is the diversity between $U_0$ determined by the single atom Wannier function
and the effective on site interaction U_eff for a multi-occupation per site.
