  Aims. Using the VIMOS Public Extragalactic Redshift Survey (VIPERS) we aim to
jointly estimate the key parameters that describe the galaxy density field and
its spatial correlations in redshift space. Methods. We use the Bayesian
formalism to jointly reconstruct the redshift-space galaxy density field, power
spectrum, galaxy bias and galaxy luminosity function given the observations and
survey selection function. The high-dimensional posterior distribution is
explored using the Wiener filter within a Gibbs sampler. We validate the
analysis using simulated catalogues and apply it to VIPERS data taking into
consideration the inhomogeneous selection function. Results. We present joint
constraints on the anisotropic power spectrum as well as the bias and number
density of red and blue galaxy classes in luminosity and redshift bins as well
as the measurement covariances of these quantities. We find that the inferred
galaxy bias and number density parameters are strongly correlated although
these are only weakly correlated with the galaxy power spectrum. The power
spectrum and redshift-space distortion parameters are in agreement with
previous VIPERS results with the value of the growth rate $f\sigma_8 = 0.38$
with 18% uncertainty at redshift 0.7.
