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.
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