The total number and luminosity function of the population of dwarf galaxies of the Milky Way (MW) provide important constraints on the nature of the dark matter and on the astrophysics of galaxy formation at low masses. However, only a partial census of this population exists because of the flux limits and restricted sky coverage of existing Galactic surveys. We combine the sample of satellites recently discovered by the Dark Energy Survey (DES) with the satellites found in Sloan Digital Sky Survey (SDSS) Data Release 9 (together these surveys cover nearly half the sky) to estimate the total luminosity function of satellites down to $M_{rm V}=0$. We apply a new Bayesian inference method in which we assume that the radial distribution of satellites independently of absolute magnitude follows that of subhaloes selected according to their peak maximum circular velocity. We find that there should be at least $124^{+40}_{-27}$ (68 per cent CL, statistical error) satellites brighter than $M_{rm V}=0$ within $300$ kpc of the Sun. As a result of our use of new data and better simulations, and a more robust statistical method, we infer a much smaller population of satellites than reported in previous studies using earlier SDSS data only; we also address an underestimation of the uncertainties in earlier work by accounting for stochastic effects. We find that the inferred number of faint satellites depends only weakly on the assumed mass of the MW halo and we provide scaling relations to extend our results to different assumed halo masses and outer radii. We predict that half of our estimated total satellite population of the MW should be detected by the Large Synoptic Survey Telescope. The code implementing our estimation method is available online.
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