Single-molecule studies can be used to study biological processes directly and in real-time. In particular, the fluorescence energy transfer between reporter dye molecules attached to specific sites on macromolecular complexes can be used to infer distance information. When several measurements are combined, the information can be used to determine the position and conformation of certain domains with respect to the complex. However, data analysis schemes that include all experimental uncertainties are highly complex, and the outcome depends on assumptions about the state of the dye molecules. Here, we present a new analysis algorithm using Bayesian parameter estimation based on Markov Chain Monte Carlo sampling and parallel tempering termed Fast-NPS that can analyse large smFRET networks in a relatively short time and yields the position of the dye molecules together with their respective uncertainties. Moreover, we show what effects different assumptions about the dye molecules have on the outcome. We discuss the possibilities and pitfalls in structure determination based on smFRET using experimental data for an archaeal transcription pre-initiation complex, whose architecture has recently been unravelled by smFRET measurements.