Exoplanet Doppler surveys are currently the most efficient means to detect low-mass companions to nearby stars. Among these stars, the light M dwarfs provide the highest sensitivity to detect low-mass exoplanet candidates. Evidence is accumulating that a substantial fraction of these low-mass planets are found in high-multiplicity planetary systems. GJ 163 is a nearby inactive M dwarf with abundant public observations obtained using the HARPS spectrograph. We obtain and analyse radial velocities from the HARPS public spectra of GJ 163 and investigate the presence of a planetary companions orbiting it. The number of planet candidates detected might depend on some prior assumptions. Since the impact of prior choice has not been investigated throughly previously, we study the effects of different prior densities on the detectability of planet candidates around GJ 163. We use Bayesian tools, i.e. posterior samplings and model comparisons, when analysing the GJ 163 velocities. We consider models accounting for the possible correlations of subsequent measurements. We also search for activity-related counterparts of the signals we observe and test the dynamical stability of the planetary systems corresponding to our solutions using direct numerical integrations of the orbits. We find that there are at least three planet candidates orbiting GJ 163. The existence of a fourth planet is supported by the data but the evidence in favor of the corresponding model is not yet conclusive. The second innermost planet candidate in the system with an orbital period of 25.6 days and a minimum mass of 8.7 Me is inside the liquid-water habitable zone of the star.
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