In a recent paper \citep fumagalli17 we reported on the detection of a diffuse H \alpha glow in the outskirts of the nearby , edge-on disc galaxy UGC 7321 observed with the Multi Unit Spectroscopic Explorer ( MUSE ) at the ESO Very Large Telescope . By interpreting the H \alpha emission as fluorescence arising from hydrogen ionised by an external ( i.e. , extragalactic ) radiation field , we estimated the UV background ( UVB ) intensity in terms of H \scriptstyle I ionisation rate ( per ion ) at z \simeq 0 to be in the range \Gamma _ { HI } \sim 6 - 8 \times 10 ^ { -14 } s ^ { -1 } . In the present work , by performing radiative transfer calculations over a large set of models of the gaseous disc of UGC 7321 , we refine our estimate and through an MCMC analysis derive a value for the photoionisaton rate of \Gamma _ { HI } = 7.27 ^ { +2.93 } _ { -2.90 } \times 10 ^ { -14 } s ^ { -1 } . In particular , our analysis demonstrates that this value is robust against large variations in the galaxy model and that the uncertainties are mainly driven by the errors associated with the observed H \alpha surface brightness . Our measurement is consistent with several recent determinations of the same quantity by a completely independent technique ( i.e. , flux decrement analysis of the Ly \alpha -forest ) , and support the notion that the low redshift UVB is largely dominated by active galactic nuclei ( AGNs ) , possibly with no need of further contribution from star forming galaxies .