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In this paper, we have investigated one of the alternative theories to darkmatter named MOdified Gravity (MOG) by testing its ability to describe thelocal dynamics of the Milky Way in vertical and transverse directions with thebaryonic matter. MOG is designed to interpret the dynamics of galaxies andcluster of galaxies without the need for dark matter. We use localobservational data such as the vertical dispersion, rotation curve, surfacedensity and number density of stars in the Milky Way to obtained the parametersof MOG and the baryonic component of MW by implementing a Bayesian approach tothe parameter estimation based on a Markov Chain Monte Carlo method. We compareour results with the dark matter model of MW. The two models of MOG and CDM areable to describe equally well the rotation curve and the vertical dynamics ofstars in the local MW. The best values for the free parameters of MOG in thisanalysis 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 thedark matter model. Our best value of bulge mass from MOG is $(1.06 \pm0.26)\times10^{10}\rm M_{\odot}$ which is consistent with the estimations formthe microlensing observations.

Testing MOdified Gravity (MOG) theory and dark matter model in Milky Way using the local observables