Comprehensive and robust analysis of galaxies found throughout cosmic time provides the means to probe the underlying characteristics of our Universe. Coupling observations and theory, spectral energy distribution (SED) fitting provides a method to derive the intrinsic properties of distant galaxies which then aid in defining galaxy populations and constraining current galaxy formation and evolution scenarios. One such population are the sub-millimeter galaxies (SMGs) whose high infrared luminosities -- typically associated with dust-obscured star formation -- and redshift distribution places them as likely key components in galaxy evolution. To fully analyze these systems, however, requires a near complete sampling of the full SED, detailed models that encapsulate the variety of physical processes and sophisticated methods for comparing the data and models. In this dissertation, we present the general propose, Monte Carlo Markov Chain (MCMC) based SED fitting routine SED Analysis Through Markov Chains (SATMC) and the insight we have gained in modeling a sample of AzTEC 1.1mm-detected SMGs. The MCMC engine and Bayesian formalism used in the construction of SATMC offers a unique view at the constraints on model parameter space that are often grossly simplified in traditional SED fitting methods. We first present the motivation behind SATMC and its MCMC algorithm. We also highlight a series of test cases that verify not only its reliability but its versatility to various astrophysical applications, including the field of photometric redshift estimation. We then present the AzTEC SMG sample and preliminary results obtained through counterpart identification, X-ray spectral modeling and SED fitting with SATMC. Finally, we present the latest work in detailed SED analysis of SMGs and how these results influence our understanding of the SMG population.

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Theories of how galaxies form and evolve depend greatly on constraints provided by observations. However, when those observations come from different datasets, systematic offsets may occur. This causes difficulties measuring variations in parameters between filters. In this thesis I present the variation in total luminosity density with wavelength in the nearby Universe (z<0.1), produced from a consistent reanalysis of NIR and optical observations, taken from the MGC, UKIDSS and SDSS surveys. I derive luminosity distributions, best-fitting Schechter function parameterisations and total luminosity densities in ugrizYJHK, and compare the variation in luminosity density with cosmic star formation history (CSFH) and initial mass function (IMF) models. I examine the r band luminosity distribution produced using different aperture definitions, the joint luminosity- surface brightness (bivariate brightness) distribution in ugrizYJHK, comparing them to previously derived distributions, and how the total luminosity density varies with wavelength when surface brightness incompleteness is accounted for. I find the following results. (1) The total luminosity density calculated using a non-Sersic (e.g. Kron or Petrosian) aperture is underestimated by at least 15%, (2) Changing the detection threshold has a minor effect on the best-fitting Schecter parameters, but the choice of Kron or Petrosian apertures causes an offset between datasets, regardless of the filter used to define the source list, (3) The decision to use circular or elliptical apertures causes an offset in M* of 0.20 mag, and best-fitting Schechter parameters from total magnitude photometric systems have a flatter faint-end slope than Kron or Petrosian photometry, (4) There is no surface brightness distribution evolution with luminosity for luminous galaxies, but at fainter magnitudes the distribution broadens and the peak surface brightness dims. A Choloniewski function that is modified to account for this surface brightness evolution fits the bivariate-brightness distribution better than an unmodified Choloniewski function, (5) The energy density per unit interval, vf(v) derived using MGC and GAMA samples agrees within 90% confidence intervals, but does not agree with predictions using standard CSFH and IMF models. Possible improvements to the data and alterations to the theory are suggested.