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Due to their higher planet-star mass ratios, M dwarfs are the easiest targets for detection of low-mass planets orbiting nearby stars using Doppler spectroscopy. Furthermore, because of their low masses and luminosities, Doppler measurements enable the detection of lowmass planets in their habitable zones that correspond to closer orbits than for solar-type stars. We re-analyse literature Ultraviolet and Visual Echelle Spectrograph (UVES) radial velocities of 41 nearby Mdwarfs in a combination with new velocities obtained from publicly available spectra from the HARPS-ESO spectrograph of these stars in an attempt to constrain any low-amplitude Keplerian signals. We apply Bayesian signal detection criteria, together with posterior sampling techniques, in combination with noise models that take into account correlations in the data and obtain estimates for the number of planet candidates in the sample. More generally, we use the estimated detection probability function to calculate the occurrence rate of low-mass planets around nearby M dwarfs. We report eight new planet candidates in the sample (orbiting GJ 27.1, GJ 160.2, GJ 180, GJ 229, GJ 422, and GJ 682), including two new multiplanet systems, and confirm two previously known candidates in the GJ 433 system based on detections of Keplerian signals in the combined UVES and High Accuracy Radial velocity Planet Searcher (HARPS) radial velocity data that cannot be explained by periodic and/or quasi-periodic phenomena related to stellar activities. Finally, we use the estimated detection probability function to calculate the occurrence rate of low-mass planets around nearby M dwarfs. According to our results, M dwarfs are hosts to an abundance of low-mass planets and the occurrence rate of planets less massive than 10M? is of the order of one planet per star, possibly even greater. Our results also indicate that planets with masses between 3 and 10 M⊕ are common in the stellar habitable zones of M dwarfs with an estimated occurrence rate of 0.21+0.03 -0.05 planets per star. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.