Fits of synthetic filament profiles. Frame (c) shows 256 generated profiles, where the noise relative to the filament peak increases logarithmically from 1% at the bottom (at Δy=0) to 20% at the top (at Δy = 255). The residuals of the least-squares fits are show in frame (a). Frame (d) shows the recovered parameter values, where the light-green lines correspond to the true input values, and the least-squares estimates are plotted in blue. For the MCMC calculations, the black lines show the mean of the MCMC samples and the red, light-grey, and dark-grey bands correspond to the [25, 75], [10,90], and [1, 99] percentile intervals, respectively. Frame (b) shows histograms corresponding to MCMC samples along the full length of the filament.