  The mass of the Local Group (LG) is a crucial parameter for galaxy formation
theories. However, its observational determination is challenging - its mass
budget is dominated by dark matter which cannot be directly observed. To meet
this end the posterior distributions of the LG and its massive constituents
have been constructed by means of constrained and random cosmological
simulations. Two priors are assumed - the LCDM model that is used to set up the
simulations and a LG model,which encodes the observational knowledge of the LG
and is used to select LG-like objects from the simulations. The constrained
simulations are designed to reproduce the local cosmography as it is imprinted
onto the Cosmicflows-2 database of velocities. Several prescriptions are used
to define the LG model, focusing in particular on different recent estimates of
the tangential velocity of M31. It is found that (a) different $v_{tan}$
choices affect the peak mass values up to a factor of 2, and change mass ratios
of $M_{M31}$ to $M_{MW}$ by up to 20%; (b) constrained simulations yield more
sharply peaked posterior distributions compared with the random ones; (c) LG
mass estimates are found to be smaller than those found using the timing
argument; (d) preferred MW masses lie in the range of $(0.6 - 0.8)\times10^{12}
M_{\odot}$ whereas (e) $M_{M31}$ is found to vary between $(1.0 -
2.0)\times10^{12} M_{\odot}$, with a strong dependence on the $v_{tan}$ values
used.
