  Evidences for late-time acceleration of the Universe are provided by multiple
probes, such as Type Ia supernovae, the cosmic microwave background (CMB) and
large-scale structure (LSS). In this work, we focus on the integrated
Sachs--Wolfe (ISW) effect, i.e., secondary CMB fluctuations generated by
evolving gravitational potentials due to the transition between, e.g., the
matter and dark energy (DE) dominated phases. Therefore, assuming a flat
universe, DE properties can be inferred from ISW detections. We present a
Bayesian approach to compute the CMB--LSS cross-correlation signal. The method
is based on the estimate of the likelihood for measuring a combined set
consisting of a CMB temperature and a galaxy contrast maps, provided that we
have some information on the statistical properties of the fluctuations
affecting these maps. The likelihood is estimated by a sampling algorithm,
therefore avoiding the computationally demanding techniques of direct
evaluation in either pixel or harmonic space. As local tracers of the matter
distribution at large scales, we used the Two Micron All Sky Survey (2MASS)
galaxy catalog and, for the CMB temperature fluctuations, the ninth-year data
release of the Wilkinson Microwave Anisotropy Probe (WMAP9). The results show a
dominance of cosmic variance over the weak recovered signal, due mainly to the
shallowness of the catalog used, with systematics associated with the sampling
algorithm playing a secondary role as sources of uncertainty. When combined
with other complementary probes, the method presented in this paper is expected
to be a useful tool to late-time acceleration studies in cosmology.
