  The High Altitude Water Cherenkov (HAWC) Observatory continuously observes
gamma-rays between 100 GeV to 100 TeV in an instantaneous field of view of
about 2 steradians above the array. The large amount of raw data, the
importance of small number statistics, the large dynamic range of gamma-ray
signals in time (1 - $10^8$ sec) and angular extent (0.1 - 100 degrees), and
the growing need to directly compare results from different observatories pose
some special challenges for the analysis of HAWC data. To address these needs,
we have designed and implemented a modular analysis framework based on the
method of maximum likelihood. The framework facilitates the calculation of a
binned Poisson Log-likelihood value for a given physics model (i.e., source
model), data set, and detector response. The parameters of the physics model
(sky position, spectrum, angular extent, etc.) can be optimized through a
likelihood maximization routine to obtain a best match to the data. In a
similar way, the parameters of the detector response (absolute pointing,
angular resolution, etc.) can be optimized using a well-known source such as
the Crab Nebula. The framework was designed concurrently with the Multi-Mission
Maximum Likelihood (3ML) architecture, and allows for the definition of a
general collection of sources with individually varying spectral and spatial
morphologies. Compatibility with the 3ML architecture allows to easily perform
powerful joint fits with other observatories. In this contribution, we overview
the design and capabilities of the HAWC analysis framework, stressing the
overarching design points that have applicability to other astronomical and
cosmic-ray observatories.
