This and companion papers by Harrington et al. and Cubillos et al. describe an open-source retrieval framework, Bayesian Atmospheric Radiative Transfer (BART), available to the community under the reproducible-research license via https://github.com/exosports/BART. BART is a radiative transfer code (transit; https://github.com/ exosports/transit; Rojo et al.), initialized by the Thermochemical Equilibrium Abundances (TEA; https://github. com/dzesmin/TEA) code (Blecic et al.), and driven through the parameter phase space by a differential-evolution Markov Chain Monte Carlo (MC3; https://github.com/pcubillos/mc3) sampler (Cubillos et al.). In this paper we give a brief description of the framework and its modules that can be used separately for other scientific purposes; outline the retrieval analysis flow; present the initialization routines, describing in detail the atmospheric profile generator and the temperature and species parameterizations; and specify the post-processing routines and outputs, concentrating on the spectrum band integrator, the best -fit model selection, and the contribution functions. We also present an atmospheric analysis of WASP-43b secondary eclipse data obtained from space-and ground-based observations. We compare our results with the results from the literature and investigate how the inclusion of additional opacity sources influences the best -fit model.