  A Bayesian analysis of 47 Ursae Majoris (47 UMa) radial velocity data
confirms and refines the properties of two previously reported planets with
periods of 1079 and 2325 days and finds evidence for an additional long period
planet with a period of approximately 10000 days. The three planet model is
found to be 10^5 times more probable than the next most probable model which is
a two planet model. The nonlinear model fitting is accomplished with a new
hybrid Markov chain Monte Carlo (HMCMC) algorithm which incorporates parallel
tempering, simulated annealing and genetic crossover operations. Each of these
features facilitate the detection of a global minimum in chi-squared. By
combining all three, the HMCMC greatly increases the probability of realizing
this goal. When applied to the Kepler problem it acts as a powerful
multi-planet Kepler periodogram. The measured periods are 1078 \pm 2,
2391{+100}{-87}, and 14002{+4018}{-5095}d, and the corresponding eccentricities
are 0.032 \pm 0.014, 0.098{+.047}{-.096}, and 0.16{+.09}{-.16}. The results
favor low eccentricity orbits for all three. Assuming the three signals (each
one consistent with a Keplerian orbit) are caused by planets, the corresponding
limits on planetary mass (M sin i) and semi-major axis are (2.53{+.07}{-.06}MJ,
2.10\pm0.02au), (0.54\pm0.07MJ, 3.6\pm0.1au), and (1.6{+0.3}{-0.5}MJ,
11.6{+2.1}{-2.9}au), respectively. We have also characterized a noise induced
eccentricity bias and designed a correction filter that can be used as an
alternate prior for eccentricity, to enhance the detection of planetary orbits
of low or moderate eccentricity.
