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Inference of the physical properties of stellar populations from observed photometry and spectroscopy is a key goal in the study of galaxy evolution. In recent years the quality and quantity of the available data has increased, and there have been corresponding efforts to increase the realism of the stellar population models used to interpret these observations. Describing the observed galaxy spectral energy distributions in detail now requires physical models with a large number of highly correlated parameters. These models do not fit easily on grids and necessitate a full exploration of the available parameter space. We present prospector, a flexible code for inferring stellar population parameters from photometry and spectroscopy spanning UV through IR wavelengths. This code is based on forward modeling the data and Monte Carlo sampling the posterior parameter distribution, enabling complex models and exploration of moderate dimensional parameter spaces. We describe the key ingredients of the code and discuss the general philosophy driving the design of these ingredients. We demonstrate some capabilities of the code on several datasets, including mock and real data., Submitted to AASJournals. 27 pages, 5 appendices, and 8 figures including one interactive figure viewable in Adobe Reader or at https://prospect.readthedocs.io/en/latest/demo.html . Prospector is available at https://github.com/bd-j/prospector . Monte Carlo samples as well as code to perform the fits and produce the figures are available in a github repo at https://github.com/bd-j/exspect

Using a compilation of 25 studies from the literature, we investigate the evolution of the star-forming galaxy (SFG) Main Sequence (MS) in stellar mass and star formation rate (SFR) out to $z \sim 6$. After converting all observations to a common set of calibrations, we find a remarkable consensus among MS observations ($\sim 0.1$ dex 1$\sigma$ interpublication scatter). By fitting for time evolution of the MS in bins of constant mass, we deconvolve the observed scatter about the MS within each observed redshift bins. After accounting for observed scatter between different SFR indicators, we find the width of the MS distribution is $\sim 0.2$ dex and remains constant over cosmic time. Our best fits indicate the slope of the MS is likely time-dependent, with our best fit $\log\textrm{SFR}(M_*,t) = \left(0.84 \pm 0.02 - 0.026 \pm 0.003 \times t\right) \log M_* - \left(6.51 \pm 0.24 - 0.11 \pm 0.03 \times t\right)$, with $t$ the age of the Universe in Gyr. We use our fits to create empirical evolutionary tracks in order to constrain MS galaxy star formation histories (SFHs), finding that (1) the most accurate representations of MS SFHs are given by delayed-$\tau$ models, (2) the decline in fractional stellar mass growth for a "typical" MS galaxy today is approximately linear for most of its lifetime, and (3) scatter about the MS can be generated by galaxies evolving along identical evolutionary tracks assuming an initial $1\sigma$ spread in formation times of $\sim 1.4$ Gyr., Comment: 59 pages, 10 tables, 12 figures, accepted to ApJS; v2, slight changes to text, added new figure and fits