Skew of the XID+ fluxes for all MIPS, PACS, and SPIRE bands in the three LOFAR deep fields. The contours show the density of the LOFAR sources whose multi-wavelength counterpart was originally undetected in the FIR. The histogram beneath the contours shows the distribution of all FIR sources in the LOFAR catalogues. The vertical lines show the flux below which a source’s posterior is dominated by the prior.