  We present the umbrella sampling (US) technique and show that it can be used
to sample extremely low probability areas of the posterior distribution that
may be required in statistical analyses of data. In this approach sampling of
the target likelihood is split into sampling of multiple biased likelihoods
confined within individual umbrella windows. We show that the US algorithm is
efficient and highly parallel and that it can be easily used with other
existing MCMC samplers. The method allows the user to capitalize on their
intuition and define umbrella windows and increase sampling accuracy along
specific directions in the parameter space. Alternatively, one can define
umbrella windows using an approach similar to parallel tempering. We provide a
public code that implements umbrella sampling as a standalone python package.
We present a number of tests illustrating the power of the US method in
sampling low probability areas of the posterior and show that this ability
allows a considerably more robust sampling of multi-modal distributions
compared to the standard sampling methods. We also present an application of
the method in a real world example of deriving cosmological constraints using
the supernova type Ia data. We show that umbrella sampling can sample the
posterior accurately down to the $\approx 15\sigma$ credible region in the
$\Omega_{\rm m}-\Omega_\Lambda$ plane, while for the same computational work
the affine-invariant MCMC sampling implemented in the {\tt emcee} code samples
the posterior reliably only to $\approx 3\sigma$.
