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We fit a parametric model comprising a mixture of multi-dimensional Gaussianfunctions to the 3.6 to 8um colour and optical photo-z distribution of galaxypopulations in the ELAIS-N1 and Lockman Fields of SWIRE. For 16,698 sources inELAIS-N1 we find our data are best modelled (in the sense of the BayesianInformation Criterion) by the sum of four Gaussian distributions or modes (C_a,C_b, C_c and C_d). We compare the fit of our empirical model with predictionsfrom existing semi-analytic and phenomological models. We infer that ourempirical model provides a better description of the mid-infrared colourdistribution of the SWIRE survey than these existing models. This colourdistribution test is thus a powerful model discriminator and complementary tocomparisons of number counts. We use our model to provide a galaxyclassification scheme and explore the nature of the galaxies in the differentmodes of the model. C_a consists of dusty star-forming systems such as ULIRG's.Low redshift late-type spirals are found in C_b, where PAH emission dominatesat 8um. C_c consists of dusty starburst systems at intermediate redshifts. Lowredshift early-type spirals and ellipticals dominate C_d. We thus find agreater variety of galaxy types than one can with optical photometry alone.Finally we develop a new technique to identify unusual objects, and find aselection of outliers with very red IRAC colours. These objects are notdetected in the optical, but have very strong detections in the mid-infrared.These sources are modelled as dust-enshrouded, strongly obscured AGN, where thehigh mid-infrared emission may either be attributed to dust heated by the AGNor substantial star-formation. These sources have z_ph ~ 2-4, making themincredibly infrared luminous, with a L_IR ~ 10^(12.6-14.1) L_sun.Comment: 44 pages, 10 figures, 6 tables. Accepted for publication in the  Astronomical Journa

Parametric Modeling of the 3.6-8 μm Color Distributions of Galaxies in the SWIRE Survey