In this paper , we have investigated one of the alternative theories to dark matter named MOdified Gravity ( MOG ) by testing its ability to describe the local dynamics of the Milky Way in vertical and transverse directions with the baryonic matter .
MOG is designed to interpret the dynamics of galaxies and cluster of galaxies without the need for dark matter .
We use local observational data such as the vertical dispersion , rotation curve , surface density and number density of stars in the Milky Way to obtained the parameters of MOG and the baryonic component of MW by implementing a Bayesian approach to the parameter estimation based on a Markov Chain Monte Carlo method .
We compare our results with the dark matter model of MW .
The two models of MOG and CDM are able to describe equally well the rotation curve and the vertical dynamics of stars in the local MW .
The best values for the free parameters of MOG in this analysis is obtained as \alpha = 8.99 \pm 0.02 and \mu = 0.054 \pm 0.005 kpc ^ { -1 } .
Also , we obtain the parameters of the generalized gNFW model in the dark matter model .
Our best value of bulge mass from MOG is ( 1.06 \pm 0.26 ) \times 10 ^ { 10 } M _ { \odot } which is consistent with the estimations form the microlensing observations .