We constrain the evolution of the rest-frame far-infrared (FIR) luminosity function out to high redshift, by combining several pieces of complementary information provided by the deep Balloon-borne Large-Aperture Submillimeter Telescope surveys at 250, 350 and 500 micron, as well as other FIR and millimetre data. Unlike most other phenomenological models, we characterise the uncertainties in our fitted parameters using Monte Carlo Markov Chains. We use a bivariate local luminosity function that depends only on FIR luminosity and 60-to-100 micron colour, along with a single library of galaxy spectral energy distributions indexed by colour, and apply simple luminosity and density evolution. We use the surface density of sources, Cosmic Infrared Background (CIB) measurements and redshift distributions of bright sources, for which identifications have been made, to constrain this model. The precise evolution of the FIR luminosity function across this crucial range has eluded studies at longer wavelengths (e.g., using SCUBA and MAMBO) and at shorter wavelengths (e.g., Spitzer), and should provide a key piece of information required for the study of galaxy evolution. Our adoption of Monte Carlo methods enables us not only to find the best-fit evolution model, but also to explore correlations between the fitted parameters. Our model-fitting approach allows us to focus on sources of tension coming from the combination of data-sets. We specifically find that our choice of parameterisation has difficulty fitting the combination of CIB measurements and redshift distribution of sources near 1 mm. Existing and future data sets will be able to dramatically improve the fits, as well as break strong degeneracies among the models. [abridged]
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