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 low-mass planets in their habitable zones that correspond to closer orbits than for Solar-type stars. We re-analyse literature UVES radial velocities of 41 nearby M dwarfs 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 HARPS radial velocity data that cannot be explained by periodic and/or quasiperiodic 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 10 M$_{oplus}$ is of the order of one planet per star, possibly even greater. ...
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