  The abilities of radial velocity exoplanet surveys to detect the lowest-mass
extra-solar planets are currently limited by a combination of instrument
precision, lack of data, and "jitter". Jitter is a general term for any unknown
features in the noise, and reflects a lack of detailed knowledge of stellar
physics (asteroseismology, starspots, magnetic cycles, granulation, and other
stellar surface phenomena), as well as the possible underestimation of
instrument noise. We study an extensive set of radial velocities for the star
HD 10700 ($\tau$ Ceti) to determine the properties of the jitter arising from
stellar surface inhomogeneities, activity, and telescope-instrument systems,
and perform a comprehensive search for planetary signals in the radial
velocities. We perform Bayesian comparisons of statistical models describing
the radial velocity data to quantify the number of significant signals and the
magnitude and properties of the excess noise in the data. We reach our goal by
adding artificial signals to the "flat" radial velocity data of HD 10700 and by
seeing which one of our statistical noise models receives the greatest
posterior probabilities while still being able to extract the artificial
signals correctly from the data. We utilise various noise components to assess
properties of the noise in the data and analyse the HARPS, AAPS, and HIRES data
for HD 10700 to quantify these properties and search for previously unknown
low-amplitude Keplerian signals. ...
